Cyclic extrusion compression angular pressing (CECAP) is a new severe plastic deformation method used to improve mechanical and metallurgical properties of metals. In this process, hydrostatic compressive stress has a considerable effect on the quality of the fabricated sample, where, as it rises, the probability of the appearance of the crack initiation on the sample is reduced. In this research, the effects of the process parameters of CECAP on magnitude and distribution of the hydrostatic compressive stress were investigated using finite element analysis (FEA) and response surface method (RSM). Temperature (T), input extrusion diameter (D), exit extrusion angle (α), frictional coefficient (µ),  and longitudinal distance of input extrusion to extrusion compression angular pressing (ECAP) region (L) were selected as input parameters, and hydrostatic compressive stress (σ) was considered as response variable. Analysis of Variance (ANOVA) was extracted to evaluate the accuracy of the developed mathematical model and determine the significant factors. Results revealed that parameters of temperature and exit extrusion angle influence the hydrostatic compressive stress (σ) considerably. Also, the effect of interaction between the parameters is significant. The optical microstructure on the CECAPed section revealed that, for point C (center of section), the grain size is larger, reaching 3 μm, while for point A (near to outer surface), the grain size reaches 1.5 μm, showing that as it becomes near to the section, the grain size tends to be smaller. In order to verify the accuracy of the study, the hardness distribution behavior was compared by the strain distribution behavior obtained from finite element method (FEM). Moreover, the hydrostatic compressive stress of the current CECAP process was compared with other investigations and a significant improvement was observed. All experimental tests and the results of other investigations showed a good agreement with FEM results.