Within the framework of the theory of developed evaporation of matter under the action of laser radiation, the problem of assessing the strength of ceramic parts of a cylindrical shape during laser punching of holes in them is considered. Analytical relations are obtained for calculating the power density of laser radiation, which leads to the destruction of the lateral surface of parts by the pressure of gaseous products as a function of the ratio of the hole radius to the radius of the part, the ratio of the radius of the part to the radius of the hole in it, and the thickness of the lateral surface of the part as a function of the power density of the acting laser radiation. Using the example of technical ceramics based on magnesium oxide P-25, the applicability of the results obtained for assessing the strength of cylindrical parts is shown. When the ratio of the hole radius to the part radius is less than 0.3, the part can be considered as an infinite body. In this case, the error in the calculations will not exceed 10 & # 37;