Meshfree methods were introduced twenty-five years ago to overcome a range of issues faced by mesh-based methods, which predominately relate to the issues of mesh-entanglement, which can result in poor accuracy. Although meshfree methods have progressed significantly over these years, the application of these techniques to real-world material forming problems is limited, despite the potential benefits they can provide over traditional mesh-based methods. This paper is concerned with the meshfree simulation of the stretch blow moulding process, which is the primary manufacturing process used to produce polymer bottles. Traditionally, the finite element method has been used to simulate this process, however, difficulties are often encountered during these simulations, which can cause reduced accuracy. In this paper, a nodally integration explicit element-free Galerkin method is formulated. Firstly, the formulation is validated through several numerical problems, which display the accuracy, and computational efficiency of the proposed method. Following this, the experimental characterisation of the stretch blow moulding process is discussed. Finally, the developed formulation is utilised to construct a validated simulation of the stretch blow moulding process. The accuracy obtained in the stretch blow moulding simulations highlights the capability of the explicit meshfree formulation, which has the potential to be applied to a wide range of large deformation phenomena.