Summary: The article presents a method of reduction of bend boundary value problems for transversely isotropic plate of the applied theory of Timoshenko type to problems of the theory of functions of a complex variable. It is assumed that the plate of constant thickness is under the action of transverse stresses. The stress state of the plate is described by the equations of equilibrium and the elasticity relations. Three types of boundary conditions defined on a curved edge plates are considered: rigidly fixed edge, hinged edge, edge free from stress. To reduce the boundary value problems to problems of the theory of functions of a complex variable certain some differential operators are introduced. A general solution of the equilibrium equation is represented by the real part of a sum of two random analytic functions and particular solutions of equation which are determined with particular boundary conditions.