The article discusses the testing of new alternative models of the biquadratic finite element of the serendipity family using the problem of torsion of a non-circular cross-section rod and compares the results obtained with the exact solution. The conversion of the Lagrange model to the serendipity model is undoubtedly a useful procedure that has been known for over fifty years. However, not all results of such a transformation satisfy users, especially supporters of physical interpretations. This concerns the value of nodal loads of uniform force (mass) (load ‘spectrum’). For a long time, it was believed that there was a single basis for each serendipity finite element – a standard one, which was obtained algebraically. Using a new approach that employs a combined algebraic-geometric method for constructing basis functions on serendipity finite elements, it has been possible for the first time to obtain alternative bases with a control parameter on a biquadratic finite element. The presence of a parameter in the basis functions of serendipity finite elements allows optimising the computational qualities of the obtained alternative models.