We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we introduce several new features adapting the strategy to suit the problem of interest. A modified fractional step method for the solution of the flow equations is applied. This approach, on the one hand, inherits the computational efficiency of the original fractional step approach, and on the other hand shows better mass conservation features. These features are particularly attractive taking into account the importance of the correct prediction of the glass product's wall thickness. A smart mesh update strategy and a simple mechanical contact scheme are introduced. In order to account for temperature-dependent viscosity, the heat equation is coupled to the mechanical model. Viscosity is obtained from the temperature field via an empirical law. The model is validated and an example modeling the processes in the final blow mold of the bottle manufacturing process is proposed.