  This article describes simulations of scattering of annihilation gamma quanta
in a strip of plastic scintillator. Such strips constitute basic detection
modules in a newly proposed Positron Emission Tomography which utilizes plastic
scintillators instead of inorganic crystals. An algorithm simulating chain of
Compton scatterings was elaborated and series of simulations have been
conducted for the scintillator strip with the cross section of 5 mm x 19 mm.
Obtained results indicate that secondary interactions occur only in the case of
about 8% of events and out of them only 25$\%$ take place in the distance
larger than 0.5 cm from the primary interaction. It was also established that
light signals produced at primary and secondary interactions overlap with the
delay which distribution is characterized by FWHM of about 40 ps.
