A four compartment model of the cardiovascular system is developed. To allow for easy interpretation and to minimise the number of parameters, an effort was made to keep the model as simple as possible. Using a standard method (Matlab function fminsearch) to calculate the parameter values led to unacceptable run times or non-convergence. Consequently we developed an algorithm which first finds the most important model parameters and uses these as a basis for a four stage process which accurately determines all parameter values. This process is then applied to data from three ICU patients. Good agreement between the model and measured arterial pressure is demonstrated in all cases.