The process of sublimation of ice particles from a rocket exhaust in the upper atmosphere is examined. Heating by solar radiation and losses of energy by means thermal radiation and sublimation are taken into account in the thermal balance of the ice particles. The time dependences of size and temperature of the ice particles are obtained. An estimation of water vapor concentration around the rocket trajectory is made. The process of sublimation of the rocket exhaust ice particles may be important for the interpretation of optical phenomena in the upper atmosphere connected with rocket launches and for propagation of disturbances at a large distance from the rocket.