Using the previously obtained equations of motion of thin micropolar elastic shells of constant thickness with an arbitrary smooth median surface, the equations of motion of an isotropic micropolar spherical shell in forces and “displacements” (kinematic parameters) are constructed. As a result, we obtained twelve equations of motion in kinematic parameters written in operator form. The equations of motion of an isotropic micropolar spherical thin shell in forces and kinematic parameters are constructed axisymmetrically. If the equations of motion of an isotropic micropolar spherical thin shell in forces and kinematic parameters assume that all the desired functions are independent of the azimuthal angle, then we obtain the necessary constraints on the displacement fields, which lead to zero values of some kinematic parameters. In this case, the model of twelve equations is reduced to six equations of motion in kinematic parameters written in operator form. In the proposed article, we have obtained an axisymmetric influence function for an unsteady oscillation of an elastic micropolar spherical shell and constructed a solution for practical calculations.