As a model for the Bénard convection in the asthenosphere<br />the problem of the hydrodynamic stability of an infinite horizontal<br />layer is calculated. The layer consists of a micropolar fluid with streich.<br />The field equations for the velocity vector, microrotation vector, microstretch,<br />microinertia, density, temperature, and pressure form a system<br />of eleven partial differential equations for the determination of eleven unknown<br />scalar functions. We succeed in decoupling the system and reducing<br />the problem to an ordinary differential equation. The analytical solution<br />can be given for the special case of a micropolar Boussinesq fluid.