This paper studies linear variable thickness circular aperture concave template theory of stiffness and strength calculation.First,set up mechanical model:Template for circular concave,outside the perimeter fixed; center has a round hole,inside the perimeter free,outside under uniformly distributed vertical load.Secondly,the establishment of mathematical model:Derivation of concave template in the axisymmetric condition,ordinary differential equation with variable coefficients of elastic curved surface,and gives the mathematical expressions of boundary conditions.Again,in view of the differential equation boundary value problem,the displacement method and the Matlab algorithm,it is concluded that the deflection of concave template function,and establish the stiffness calculation condition of concave template.Then,determine the concave template on the bending moment and the maximum bending moment and stress,so as to establish a concave template strength calculation conditions.Finally,numerical examples.This paper presents the function solutions,to change law of control concave template section variable parameters.In this way,not only highlight the interdependent relationship between the quantity of each,and optimization,and discussion and application.The result is suitable for uniform,continuous,isotropic material artifacts.Because in the process of calculation and data processing with error,so the formula is similar.