Receptor dependent clathrin-mediated endocytosis (CME) is one of the most important endocytic pathways for the internalization of bioparticles into cells. During CME, the ligand-receptor interactions, development of clathrin-coated pit (CCP) and membrane evolution all act together to drive the internalization of bioparticles. In this work, we develop a stochastic computational model to investigate the CME based on the Metropolis Monte Carlo simulations. The model is based on the combination of a stochastic particle binding model with a membrane model. The energetic costs of membrane bending, CCP formation and ligand-receptor interactions are systematically linked together. We implement our model to investigate the effects of particle size, ligand density and membrane stiffness on the overall process of CME from the drug delivery perspectives. Consistent with some experiments, our results show that the intermediate particle size and ligand density favor the particle internalization. Moreover, our results show that it is easier for a particle to enter a cell with softer membrane. The model presented here is able to provide mechanistic insights into CME and can be readily modified to include other important factors, such as actins. The predictions from the model will aid in the therapeutic design of intracellular/transcellular drug delivery and antiviral interventions.