A tumour invasion model has been developed to examine the influence of diffusible matrix metalloproteinases (MMPs) and the mediated proteolysis of non-diffusible, membrane type MMPs (MT-MMPs) on tumour growth and morphology via haptotaxis. Our results are the first to explore the influence of localized degradation of extracellular matrix (ECM) by MT-MMPs on the morphology of tumours growing in nutrient-rich and nutrient-poor microenvironments. Two-dimensional numerical simulation, using a level-set-based tumour host interface-capturing method, reveals that haptotaxis due to ECM degradation by MMP causes greater instability than with ECM degradation by MT-MMP in low-nutrient environments, even at low proliferation rates; whereas the resulting morphologies are similar for high apoptosis rates. Our simulation results show that while haptotaxis leads to completely different tumour growth rates and morphologies depending on proliferation and apoptosis rates in low-nutrient environment, there are no significant variations when we compare the haptotaxis due to ECM degradation by MMP and MT-MMP, except for low proliferation rates. Focusing on the differences between MMP and MT-MMP mediated effects; our study has important implications in MMP-target validation and MMP-inhibitor-drug development for anti-cancer clinical trials.