This work deals with the creation of a stochastic algorithm for aa-tRNA competition during translation using an abstraction of the biological model. The major challenges were to manage aa-tRNA specie specific input information in order to deal with eventual transient aa-tRNAs pool variations and tracking the stochastic individual state behavior of all molecules. The algorithm based on a Gillespie’s exact method with two additional Monte Carlo iterations was developed to avoid states explosions due to species combinations. The validation of the Algorithm for aa-tRNAs competition was tested for each codon, simulating a single ribosome decoding constantly the same codon with a constant aa-tRNAs pool in Escherichia Coli. The probabilities of erroneous insertion and amino acid insertion time verified successfully the same linear increasing tendencies for greater pseudo-cognate and near-cognate aa-tRNA competition to match a codon, as found in Fluitt and Bosnacki works. Moreover, the Algorithm ability to track individual molecules of aa-tRNA during the simulation was proven by recovering this identical tendency in the case of the mean non-cognate, pseudo-cognate and near-cognates total arrivals before a single amino acid introduction versus the mean insertion time for each codon. Furthermore, this ability was used to recover individual insertion probabilities of each aa-tRNA species for each codon. The work ends by suggesting further eventual algorithm applications that can be performed.