In this work we present a parallel polarizing phase shifting interferometer based in a Double Cyclic Interferometer (DCSI) to analyze transparent samples. This system has the advantage of generating four beams that can interfere properly; this can reduce the number of captures needed in phase shifting interferometry. The interferometric system generates two π-shifted interferograms, which are recorded by the CCD camera in a single-shot. For the processing of the optical phase data map, a parallel phase shift can be generated by placing a linear polarizer covering two patterns. We analyze the cases of four patterns with arbitrary shifts captured in two shots. The unwrapped phase is processed by Kreis methods. Experimental results obtained by the proposed interferometer are presented.