Abstract <p>This work is devoted to considering two problems on the floating stability of rectangular and triangular bodies onto which a semicircular bar is symmetrically placed in the initial equilibrium position. The main principles of stability research by analytical statics methods are presented, and the necessary expression for the potential energy of a floating body with an additional solid load in the general form is constructed. For these problems, the most interesting variant of a movable semicircular bar relative to the floating body is considered, and the case when they are rigidly connected to each other is discussed. The stability conditions obtained, taking into account the introduction of dimensionless parameters in each of the designated cases for both problems, are compared with each other, as a result of which similarities and differences in their formula representations are revealed. These conditions, together with the feasibility condition, are displayed in a visual graphical form as families of boundaries of stability regions on the plane of two dimensionless parameters at different values of the third parameter. The results found are of fundamental importance for analytical mechanics and stability theory and they can find their application in practice.</p>