The results of computer simulation of the film cooling efficiency on a concave surface with coolant supply through inclined round holes in shallow trenches are presented. The calculations were carried out in a range of blowing ratio m from 0.56 to 1.97 using the commercial computer package ANSYS CFX and the SST turbulence model. In the region between the trenches, the average (within an individual strip) cooling efficiency hardly changes at all in the transverse direction for all blowing ratios. Downstream of the second trench, the average cooling efficiency is nonuniform across the width of the concave surface and increases with the blowing ratio. The local (spot) cooling efficiency is nonuniform across the plate and becomes more uniform with an increase in the blowing ratio. For low blowing ratios, the number of local maximums in the cooling efficiency behind the first trench is equal to the number of film cooling holes. For m ≥ 1.12, the cooling efficiency is almost uniform and close to unity immediately behind the first trench, while it reduces on the side strips behind the second trench. The effectiveness of film cooling on a concave surface with two trenches has been demonstrated to be 5-11% lower than that on a flat surface under the same conditions.