Transendothelial migration is a crucial process of the metastatic cascade in which a malignant cell attaches itself to the endothelial layer forming the inner wall of a blood or lymph vessel and creates a gap through which it enters into the bloodstream (or lymphatic system) and then is transported to distant parts of the body. In this process both biological pathways involving cell adhesion molecules such as VE-cadherin and N-cadherin, and the biophysical properties of the cells play an important role. In this paper, we present one of the first mathematical models considering the problem of cancer cell intravasation. We use an individual force-based multi-scale approach which accounts for intra- and inter-cellular protein pathways and for the physical properties of the cells, and a modelling framework which accounts for the biological shape of the vessel. Using our model, we study the influence of different protein pathways in the achievement of transendothelial migration and give quantitative simulation results comparable with real experiments.