Is there a polite way for an artist to accept compliments? Is it rude to be modest?

Smile, say thanks and accept the compliment.

The strangers are praising your creations, not asking for your resume. Such compliments are sincere and said with kindness; accept them with gratitude, and use them to build your self-confidence as an artist.

Make eye contact, smile warmly, and nod in thanks.
or
Say, “I’m so pleased you like it.”
or
Say, “Thank you for your kind words.”

Funny, I tend to go the other way when people compliment me and say, “Well, I’ve been doing this for 20 years.” It’s an explanation and a self-disparagement.

I think it’s fine to say whatever you want to say but for me, it’s also a question of being distracted from my work. If you don’t want to talk much, a simple “Thank you” is just fine.

You can wear a novelty t-shirt or have a sign saying leave me alone. Or thanks or be creative.

Smile and say thank you. Free and easy way to deal with it. No need to start a discussion or engage in conversation.

Someone is complimenting you on your artwork, it doesn’t matter if you’ve been drawing/painting for 5 days or 25 years, they are saying they enjoy what you have created, now. I liken your response to a woman who is complimented on her clothing and says “oh this dress, it only cost me $10 dollars at the second-hand store.” Let yourself receive the compliments for what they are, expressions of enjoyment of your creation.

I knew a girl named Hanneke, who was a very good artist at a very early age. When someone complemented her, saying how good her work was, she’d just say, “So..?”

(No, I don’t recommend you do that—but coming from her, it was a bit funny somehow).

Just say, “Thank you.” With or without cordiality or eye contact. But DO say it.

Set up a bucket filled with crumpled Monopoly™ money behind you. Perhaps people will be less effusive in their praise if they think they need to deliver it with cash.~

Aside from that, though, there’s no need for you to engage with people you don’t want to – ever. It’s your time, your space, your creation. You don’t even need to nod. Let people think what they will; be at peace in your own world and feel free to ignore the ignorant, whether it’s their praise or their criticism that’s ignorant. (For that matter, you may wish to wear headphones – even if you listen to nothing at all through them – as a way to emphasize that you’re not there for conversation or to respond to comments.)

Ssmile, nod, and say “you’re too kind!”.

Just say “Thank you.” Self-deprecation sounds false. Denying your skill makes it sound like the complimenter is stupid for liking it. Saying you’ve been at it forever sounds like “Well, of course it’s good” (how could it be otherwise?). Saying you’re just a beginner sounds like you’re fishing for more affirmation. Just say “Thank you.”

If they ask you things like “Are you an art student?” and “How long have you been studying drawing?” then you can tell them how new you are to it and where you’re getting your instruction.

Jeruba’s advice is best.

Saying ‘Thank You” even works in a nonchalant way if you do not want the person’s advances

I understand what you mean. You feel dishonest, because in your eyes or way of thinking you feel like it’s cheating. No real creativity. I use to draw really well in high school. I felt confident in my ability until I saw my cousins art work. I was great at copying photos from magazines or even doing portraits of animals or people. But I sucked at creating things from my own mind. I could envision things. Angels with glorious wings or exotic looking animals but I couldn’t transfer it down on paper. I could only copy something that was right before me. You could ask me to draw a cat. I know what they look like, and I can envision them in detail but again, I couldn’t transfer what I see on paper. So when people would compliment my art work, I felt like a fraud. I could ask my cousin to draw a mountain side with water falls and large flying exotic birds and he could create something better than what was in my mind. No visual aids.
So to me. He was an artist. He had the ability to create. I had the ability to copy. So I lost interest. (By the way, he could act, sing opera, and write songs)
But to other people, they thought I was talented.

Just remember, that they probably think compared to them, you are very talented or that your style is something they appreciate. So accept the compliment. I may be just a human fax machine but there are many who can’t even do that. There are just different levels of talent and everyone has their own style. Remember there are paintings in museums that some people think is trash, and some people appreciate. Beauty is in the eye of the beholder.
So by not taking their compliment you are saying their taste must be crap.
Say thank you and that you are glad they appreciate your work.

I used to be a cake decorator.
I was very good. Compliments felt great.
I can’t draw to save a life.
I have never had control of my hands for that. I am stiff, not my joints, my muscles. I am unable to use subtle control with pencil, chalk, etc. I have had beautiful scenes in my head I could not through any effort make visible.

Following those tutorials may seem like cheating to you, but only someone with talent could make use of them to begin with.

Cake decorating requires it’s own kind of talent. It uses the very thing which makes me unable to draw. To make something take shape with icing requires squeezing, with a pressure which is constant, though not consistent.

Accept compliments with the knowledge that you do indeed deserve them. These people are not your mommy. They don’t feel a need to boost your confidence. If they compliment you, they like what they see. It doesn’t matter if you are a beginner, a pro, or a monkey. If you’re good, people will see that, and some will say so.

Excellent answer, @Patty_Melt.

Anyone can learn how to cook, but doing so doesn’t make someone a chef. Anybody can take a picture – it’s nothing more than pointing and clicking – but it takes talent to become a photographer. The same is true for art; it’s easy to learn how to draw, just taking shapes and shades and putting them on paper, but being an artist is something very different.

@rockfan, it sounds as if you have artistic abilities that are being recognized by other people.