Recent "hydraulic bomb" and "confined sleeve" tests on transparent armour glass materials such as borosilicate glass and soda-lime glass showed that the glass strength was a function of confinement pressure. The measured stress-strain relation is not a straight line as most brittle materials behave under little or no confinement. Moreover, borosilicate lass exhibited a stronger compressive strength when compared to soda-lime glass, even though soda-lime has higher bulk and shear moduli as well as apparent yield strength. To better understand these experimental findings, a mesoscale phase field model is developed to simulate the nonlinear stress versus strain behaviours under confinement by considering heterogeneity formation - under triaxial compression and the energy barrier of a micro shear branding event (referred to as pseudo-slip) in the amorphous glass. With calibrated modelling parameters, the simulation results demonstrate the the developed phase field model can quantitatively predict the pressure-dependent strength, and it can also explain the difference between the two types of glasses from the perspective of energy barrier associated with a pseudo-slip event.