Simulations of four JET type I ELMy H-mode discharges in a triangularity scan are carried out using the JETTO integrated modelling code with a predictive core and pedestal model that includes the effect of ELMs. The pedestal width is calculated using a theory-motivated model based on magnetic and flow shear stabilization and the pressure gradient is limited by MHD ballooning instability. The Mixed Bohm/gyro-Bohm anomalous transport model is used in the plasma core while ion thermal neoclassical transport is used in the pedestal. It is found that the predicted plasma profiles reproduce the observed plasma proles. An MHD stability analysis is carried out for the discharges in the triangularity scan using HELENA and MISHKA codes, which include finite-n ideal ballooning, finite-n ballooning, and low-n kink/peeling modes. It is found that higher triangularity plasmas have easier access to the second region of ballooning mode stability, which allows the edge pressure gradient to increase to higher levels.