In this work we present the vectorisation of a new complex numerical algorithm to simulate the lubricant behaviour in an industrial device issued from tribology. This real technological problem leads to the mathematical model of the thin film displacement of a fluid between a rigid plane and an elastic and loaded sphere. The mathematical study and a numerical algorithm to solve the model has been proposed in the previous work [9]. This numerical algorithm mainly combines fixed point techniques, finite elements and duality methods. Nevertheless, in order to obtain a more accurate approach of different real magnitudes, it is interesting to be able to handle finer meshes. As it is well-known in finite element methods, mesh refinement carries out a great increase in the storage cost and the execution time of the algorithm. It is precisely this computational cost problem what has motivated the authors to try to increase the performance of the numerical algorithm by using high performance computing techniques. In this work we mainly apply vectorisation techniques but also we present some preliminary partial results from the design of a parallel version of the algorithm.