A theoretical investigation of heat and mass transfer during evaporation in a wet capillary structure in contact with a heating wall is presented. The wall has grooves by which the vapour is removed. Setting and results of the numerical investigation of the mathematical model (stationary two-dimensional boundary problem with a free boundary corresponding to the surface of the interphase transition inside the capillary structure) are given. Calculations performed at different heat and hydraulic loads allow one to trace the phases of the process evolution : origin and growth of vapour zones (bubbles). The evaporation intensity distribution and functional characteristic of the capillary structure have been found.