In this study, the accuracy achievable in the parameter estimates of a three-element linear model for the systemic vascular bed is considered. The model neglects inertial effects and includes only three elements representing arterial compliance, peripheral resistance and venous compliance, in agreement with recent sensitivity investigations. Parameter estimation starts from arterial and right atrial pressure signals generated by a closed-loop simulator of the cardiovascular circulation and corrupted with normal noise to account for measurement errors. In this way, the influences of a wide variety of circulatory conditions were investigated. The results achieved give evidence that arterial compliance is generally well estimated, while venous compliance is more variable, particularly at high peripheral resistance when measured signals appear to be less sensitive to this parameter. However, presence of cardiac disease, such as heart failure and valvular stenosis has minimal influence on compliance estimates. These results suggest that this simple model can be conveniently applied even under noisy conditions.