This work deals with the creation of a stochastic translation algorithm capable of encompassing the reactions for translation initiation, elongation and termination in a unified framework based on Gillespie's algorithm. By looking at reactions from the point of view of the ribosome. That is as transitions from one of the 64 available codons to the next, the system was reduced to 64+2m equations, with m being the number of mRNA species in the system. Using this approach, the system no longer scales with molecule numbers or mRNA length, increasing only by 2 reactions for each additional mRNA species. The algorithm was validated by replicating the results from the Heinrich- Rapoport (H-R) model as well as the Zouridis-Hatzimanikatis (Z-H) model. The stochastic protein translation model by Mitarai et al. was also recovered using the algorithm. Furthermore the use of the stochastic translation algorithm allows for a complete analysis of the noise of the system. In the H-R model it is shown that increased noise levels in polysome sizes around the phase shift correspond to the fast increase in polysome size observed in their results. From comparing the Z-H model to the stochastic translation algorithm, it was shown that as protein production reaches its maximum with respect to polysome size, protein noise reaches a minimum. The report ends by suggesting further work that can be accomplished by using this algorithm and the questions that can be answered, opening the door to several interesting experiments