The industrial manufacturing of glass containers consists of several phases, one of which is the blowing phase. This paper describes the development of a numerical simulation tool for this phase. The hot liquid glass is modelled as a viscous fluid and its flow is governed by the Stokes equations. We use the boundary element method to solve the Stokes equations and obtain the velocity profile at the glass surface. The movement of the surface obeys an ordinary differential equation. We use the Euler forward method to perform a time integration step and update the shape of the glass surface. All calculations are performed in three dimensions. This allows us to simulate the blowing of glass containers that are not rotationally symmetric. The contact between glass and mould is modelled using a partial-slip condition. A number of simulations on model glass containers illustrates the results. Please note that this article has three supplemental video files: