The paper considers a system analysis problem, which consists in constructing a structural connection between solutions to the biharmonic equation and the Laplace equation in polar coordinates. Namely, the integral representation of the biharmonic Poisson kernel via the Poisson kernel in a unit disk is constructed. It is shown that the integral representation of the biharmonic function can be considered as an average of the Abel–Poisson integral with a density distribution. It is established that the structural connection between the deviations of the operators under study from their boundary values contains a similar deviation for the biharmonic Poisson integral in Cartesian coordinates.