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My Master of Science degree thesis, where a numerical procedure is developed to analyze optimum autofrettage pressures for certain working pressures of thick-walled cylinders made from materials exhibiting bauschinger effect (BE). A combined numerical-analytical procedure are also developed to analyze optimum C-Test forces that best simulate autofrettaged cylinder including BE. The procedure may be used later in crack propagation analysis. Using ABAQUS version 6.9 finite element package and without any required subroutines the designer can simply follow the procedure to get optimum autofrettage point. Previous publications covering the C-Test did not include BE. A Matlab M-file is written using Combined Numerical-Analytical Procedure, and Optimum C-Test compression force is obtained. The combined numerical-analytical procedure shows complete agreement with numerical one. Two optimization procedures are used. It is time savings to use the second optimization procedure which uses quadratic interpolation rather than using the first one which searches for the optimum by iterations.