The paper presents the results of computer simulation of film cooling behind two rows of trenches on an adiabatic flat plate with coolant supply through inclined round holes in the trench. The calculations were carried out in the wide range of injection parameter from 0.4 to 2.2 using the commercial computer package ANSYS CFX 14 and the SST turbulence model. It was found that for the injection parameter m > 0.6, the asymmetry in the film cooling effectiveness is observed behind the second trench increasing with the injection parameter growth. This is explained by the unsteady nature of interaction of the cooling jets discharged from holes of the first and second rows. In the area between the first and second rows of trenches near the end “strips”, the film cooling effectiveness is 5–10% higher than near the middle ones, however, behind the second trench it is 8–20 % lower, due to the staggered arrangement of the injection holes in trenches. For all injection parameters, the globally-averaged film cooling effectiveness near the end “strips” of the adiabatic surface is lower than that near the middle ones.