Severe plastic deformation (SPD) induced by conventional forming processes such as extrusion has a significant effect on texture evolution and strength of metals. Conventional twist extrusion (TE) process can be used to produce ultra-fine grained (UFG) structures without introducing any significant change in the overall dimensions of the sample. However, the commercialization for industrial usage has been limited because of production efficiency and non-uniform distribution of grain refinements. In order to overcome these difficulties a new process called nonlinear twist extrusion (NLTE) has been introduced recently where TE mold channel is modified to restrain strain reversal and rigid body rotation of the workpiece. Prediction of the texture evolution in these processes is crucial for mold design and process parameters. In this work, the texture evolution during NLTE and TE processes are investigated through crystal plasticity finite element method. Single copper crystal which has a billet form is fully extruded through the TE and NLTE mold models separately. In addition to spatial stress and strain evolution investigations, the orientation differences and texture evolution of extruded billets are examined for two different initial orientations of single copper crystal. Moreover, the deformation histories at different locations of the sample are analyzed with crystal plasticity finite element method (CPFEM) to compare the performance of both techniques.