The paper considers a system of three linear inhomogeneous algebraic equations describing the change in the free angular velocity of a rigid body in space. The system of equations has a known analytical solution. The concept of monotonic stability of the solution of a system of algebraic equations is considered. The aim of the work is to obtain and analyse the conditions for monotonic stability of the angular velocity of a rigid body over a finite time interval of motion. In this case, the condition of monotonic decrease of angular velocity is obtained, a qualitative analysis of the convexity of the curve describing the change in angular velocity of a rigid body is carried out, and the condition of non-negativity of the second derivative, the condition of decrease of the second derivative, the condition of convergence of the angular velocity to a zero value and the condition of stabilization of the solution at the end point are formulated. The work provides an example confirming the reliability of the analytical conditions of monotonic stability obtained in it. #CSOC1120.