The Monte Carlo method was employed to obtain the response of a position sensitive gamma ray detector. The basic unit consists of a scintillator bar coupled to two photon detectors. Determination of the position of interaction is obtained from the ratio of the light intensity measured at each extremity of the bar. Association of two or more detectors of this type can be used to build a system with potential use in positron emission tomography. For practical purposes, a CsI(Tl) bar with dimensions of 15×1×1 \thinspacecm³ was considered. Simulations were performed with the GEANT4 toolkit, using the physical processes of low-energy electromagnetic extension. Light attenuation coefficient and energy resolution of CsI(Tl) bars were included according to data found in the literature. Results obtained from detector irradiation with 511 keV annihilation photons indicate that the position of interaction can be determined with uncertainty of 3 mm. Simulations of positron sources placed between two detectors were also performed and two dimensional images were obtained.