The paper presents theoretical studies of a new deformation process combining the stages of equal-channel angular pressing (ECAP) and the Linex scheme. To analyse the resulting deformation forces, the stages of pressing in a matrix and compression by a chain conveyor are separately considered. Equations were provided for determining the forces acting on the drive pulley, ECA matrix, and chain element link. A trial calculation and comparative analysis with the previously known rolling-ECAP process showed that the new ECAP-Linex process allows for a stable deformation process with lower forces and a smaller channel junction angle in the matrix. The values obtained by equations are verified with computer simulation using the finite element method in the Deform program. A comparison of values showed that the force values in the calculation and simulation have a high level of convergence. For all three considered parameters, the difference value did not exceed 3%.