In this paper, the boundary value problem of circular plate bending is discussed according to the improved theory. In area $D$, the plate is continuously loaded with force and moment, and the edge is once rigidly clamped and the second free. The entire boundary value problem is translated into the search for two holomorphic functions $\varphi_0(z)$ and $\psi_0(z)$ in the domain $D$. The boundary values of the holomorphic functions themselves appear in the equation from which we complete the function.