The paper presents theoretical studies of a new deformation process combining the stages of equal-channel angular pressing (ECAP) and the “Linex” scheme. For correct finite element modeling of the process, a technique with sequential input for the calculation of conveyor links is presented. To analyze the efficiency of metal processing, the main parameters of the stress–strain state are considered: equivalent strain, equivalent stress, and average hydrostatic pressure, as well as the deformation force on the main elements of the combined process: pulley, matrix, and conveyor link. To analyze the resulting deformation forces, the stages of pressing in a matrix and compression by a chain conveyor were separately considered. Equations for determining the forces acting on the drive pulley, ECA matrix, and the chain element link were obtained. Comparison of values showed that the force values in the calculation and simulation have a high level of convergence. In all three considered details, the difference value did not exceed 10%. The variational modeling allowed to determine the optimal values of the main technological and geometric parameters of the process.