A variant of the equal channel angular pressing (ECAP) process, the so-called T-ECAP is examined in this work. In T-ECAP the material is pushed from one channel into another one, which is open in the two perpendicular flow direction. With the help of a new flow line function, the deformation field is examined in details. The proposed flow function contains just one additional parameter compared to the previous one which was used to describe the material flow during non-equal channel angular pressing (NECAP). The new parameter permits to extend the flow line into the exit channel; outside the intersection zone of the two channels. This improvement is based on experimental flow lines obtained in T-ECAP of aluminum. The new flow function was employed to analyze the experimental flow trajectories and to characterize the corresponding plastic deformation field. The evolution of the crystallographic texture was also simulated using the new flow function. The gradient in the texture across the thickness of the extruded sample was examined and simulated. Excellent agreement was obtained between the simulated and experimental crystallographic textures in T-ECAP of Al-1050, validating in this way the proposed flow function.