This is a pretty common complaint which stems from people learning that pushing off with their legs, or so called "power running", puts a lot of stress on a small muscle group. Your calves are engaged when performing the push off.
If instead if you pick your feet up in more of a controlled fall forward, the big quad muscles are engaged in a task they can more than handle.
Another reason the calves can be sore is due to a change in form. If you progress from a heel-to-toe to a more mid foot landing you will probably be sore in new and wonderful places. Your body is adapting to the changes and you are feeling the results.
To ensure you do not hurt yourself it is prudent to perform short duration but frequent runs. This ensures your body has multiple small recovery periods instead of a few larger ones.