I have biliary calculees (stones). is there any medicine that could disolve and eliminate these stones?

Not efficiently: Prior to the laparoscopic cholecystectomy/ercp era there was a class of medications that were tauted to be able to dissolve gallstones if they had specific criteria(3 or less, cholesteral type stones less tha 1 cm) . However, this medication(a bile salt dissolution agent) if successfull had to be taken the rest of your life, otherwise the stones would return.

Biliary stones: There are a few products used to try to dissolve gall stones. The most common one is called ursodiol. It is usually only used for more difficult situations, like symptomatic stones when there are medical reasons for not undergoing surgery. You would never take it if you are not having symptoms. It has side effects, but if you're having a lot of symptoms and don't want surgery, it may be reasonable.