Abstract <p>A refined transformational mathematical model is proposed to describe the deformation process of a strip having fixed and loose segments along its length. It is assumed that the strip in the fixed segment is attached to a support element, which has displacement components prescribed (known) at the points of attachment to the strip, which allows, in particular, simulating the process of kinematic loading of the strip during tensile and compression tests. To describe the process of deformation of the loose segment of the strip, the tangential displacements are approximated by a third-degree polynomial along the transverse coordinate, and the deflection is approximated by a second-degree polynomial. In the fixed segment, the approximations of the displacements that were assumed for the loose segment are transformed into other approximation functions along the transverse coordinate due to their compliance with the kinematic conditions of the two-sided attachment to a support element with prescribed displacements. The conditions for the kinematic coupling of the fixed and loose parts of the strip are formulated using the D’Alembert–Lagrange variational principle, and the equations of equilibrium and motion of the fixed and loose segments of the strip are obtained.</p>