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Invasion of the surrounding tissue is one of the hallmarks of cancer. Solid tumours have a reciprocal relationship with the surrounding microenvironment, a complex tissue composed of extracellular matrix and other multiple distinct cell types. Prote- olytic degradation and remodelling of the extracellular matrix is essential for cancer cells to be able to invade. Important matrix degrading enzymes include the matrix metalloproteases (MMP) and the urokinase plasminogen activator (uPA). This thesis has investigated the complex process of cancer growth and spread that occur across several different spatial scales, in order to gain a better understanding of the key processes involved during invasion. At first, we tested our modelling concept by applying a level-set method to a moving boundary problem. Later, a multi-scale mathematical model of cancer invasion was developed by coupling the urokinase plasminogen activation (uPA) system with a two-scale computational modelling technique. This approach allows us to investigate cancer invasion not only at the macroscopic tissue level, but also at the microscopic cellular level. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer known as tumour infiltrative growth patterns (INF).