This paper provides an engineering J estimation equation for cylinders with finite internal axial surfacecracks under internal pressure. The proposed equation is the J estimation equation based on deformation plasticity using Ramberg-Osgood (R-O) materials. Based on detailed 3-D FE results using deformation plasticity, plastic influence functions for fully plastic J components are tabulated for practically interesting ranges of the mean radius-to-thickness ratio, the crack depth-to-length ratio, the crack depth-to-thickness ratio. the strain hardening index for the R-O material, and the location along the semi-elliptical crack front. Based on tabilated plastic influence functions, the J estimation equation along the crack front is proposed and validated for R-O materials. Good agreements between the FE results and the proposed J estimation provide confidence in the use of the proposed method to elastic-plastic fracture mechanics of pressurized piping.