This work is focused on the first step of the extrusion blow moulding process as part of a global optimisation process encompassing several steps: optimisation of the part thickness, optimisation of the parison thickness that will guarantee the specified thickness profile and optimisation of the extrusion conditions (namely, the sequence of the die mandrel movements) required to obtain the optimal parison thickness distribution. A high density polyethylene (HDPE) extrusion blow moulded tamper evident container was studied using a finite element based analysis (FEA) in order to determine the optimized thickness distribution required for the blown part, considering its mechanical specifications. Several tests corresponding to the requirements for UN homologation for dangerous substances transportation were performed using a commercial software. Non-linear models were used to better describe the mechanical part behaviour. The results obtained at this stage were used to redesign the blown part. In future work this optimised design will be used as an input for optimising the subsequent stages.