The possibilities of using and embedding kinematic trapezoid modules with curvilinear boundaries of different shapes were explored. Based on the energy method, the generalized formulas for calculating the power of deformation forces inside the axial trapezoidal kinematic module were derived. Different types of selecting the functions that describe a curvilinear boundary of the axial trapezoidal module were identified. We have analyzed the possibilities of using known techniques for the linearization of integrand dependences in order to calculate the power of deformation forces when it is impossible to obtain a given magnitude in the form of an analytical function. The ways to derive engineering formulas for the computation of components of reduced pressure inside an axial trapezoidal kinematic module were proposed. Based on the energy method, we obtained formulas for the calculation of a step-by-step change in the shape of a semi-finished product under assumption within the axial trapezoidal kinematic module. We modeled the process of combined extrusion of hollow parts with a flange and established regularities in shape formation depending on geometrical parameters. The data about a step-by-step change in the shape of a semi-finished product during deformation were obtained. A comparative analysis of calculation schemes for the rectilinear trapezoidal kinematic module and with a curvilinear boundary under assumption within the studied module was performed. It was confirmed that the reported ways for obtaining engineering formulas, as well as the algorithm for the calculation of processes of combined extrusion that is based on them, simplify the development of technological recommendations. This applies both to determining the force mode of extrusion and preliminary assessment of a change in the shape of a semi-finished product with the possibility to control a metal outflow in the process of deformation