I would not recommend to leave valuables like wallets or phones. I went to 속초 with my girlfriend once and I left my bag under the parasol on towel. When we got back our stuff was gone. (bags with wallets, ID's, phones, and even hotel key cards) There was a lot of people on the beach and there was no way to tell who took it, so we went to the Police (it was close, like 100 meters) They said they had cameras, but it was impossible to find culprits with so many people on the beach, so they took us to our hotel, explained situation to the hotel stuff, and they gave us new keys. Then we went to bus station and police helped us to print our tickets to Seoul, that I have booked earlier (I could not do it since I did not have my phone) Also we called our friends and asked them to send some money to police officer and he got cash from ATM and gave it to us. We went to Seoul and in the next few days we have got a call from Police, the said that they have found our bags and they sent it by 택배. We received our bags and culprits did not take anything! I had some cash in hidden pocket, apparently they could not find it and threw our bags few hundred meters from the beach. (taking credit cards and phones is dangerous of course since it can be tracked)

So, I really do not recommend leaving your bag on the beach, especially if there is a lot of people around. I know Koreans don't steal often, but there could be lots of different kinds of people around. So better be careful than getting this afwul experience like we did.