In 3D positron emission tomography the scatter effect is a significant physical factor degrading image quality. The advancements in computing that occurred the last decades al lowed us to simulate the scatter coincidences fast and ef ficiently. The main concern now is how accurately do we simulate the scatter events. The scope of this project is the implementation and the evaluation of a scatter simulation algorithm that would be able to simulate the scat ter ef fect more precisely than the existing ones. One way to simulate the scatter distribut ion is with an algorithm, first published by Watson and Ollinger, that is based on the Klein-Nishina formula. These methods have been implemented taking into account only the single scatter events (where a photon scatters once in the at tenuation medium). Multiple scatter is generally taken into account by some scaling or filtering procedure. Their main advantages are short computational time and relatively good precision compared to previous more heuristical methods. Although these single scatter algorithms have been effective there are cases where their results are not that accurate. For low energy thresholds and large at tenuation mediums multiple scatter is increased. Given that a significant percentage of people are over -weight (thus the at tenuation medium has large volume) we should consider introducing multiple scatter events in our simulations. Moreover, the distribut ion of all scatter events is broader than the one of single scatter events therefore even if the single scatter distribution is scaled it will not match the total scatter one. In previous work by C. Tsoumpas et al, a new scatter simulation algorithm was developed that attempts to approximate the total scatter distribution by taking into account the case where the one annihilated photon is scattered twice and the case where both annihilated photons are scattered once. These two cases describe the double scatter events and by introducing them into our scatter simulation algorithm we aim to obtain a better approximation of the total scatter distribution. In this thesis we have improved this double scatter simulation algorithm in two important ways. When both annihilated photons scatter they acquire a favourable polarization direction with respect to each other and this influences thei r detect ion probabilities, especially when low energy photons are detected. In the algorithm that we implemented we considered this effect by using the polarized Klein-Nishina formula for this case. In addition, we investigated and validated the need to introduce extra solid angle factors in the implementation. The whole implementation is based on the STIR library (Software for Tomographic Image Reconstruction) written in the C++ programming language. Scatter events can also be simulated by Monte Carlo simulation packages such as SimSET. SimSET is a public domain package designed to simulate positron emission tomography (PET) (and Single Photon Emission Tomography) and was used extensively in this project. Monte Carlo packages because of their ability to exclude any unknown physical parameter they can simulate physical processes like the ones that take place in PET very accurately. Thus they were essential for the evaluation of our scatter correction algorithm. The reason why Monte Carlo packages are not used inclinical practice instead of the model-based methods is that they demand a large computational time. Besides Monte Carlo packages we also per formed a series of experimental scans in order to evaluate our scatter simulation algorithm. The tomograph used for the experiments was the ECAT 962 used in a 3D mode. / -