This paper presents an analytical function to predict the performance of a paraboloidal dish solar concentrator with a cavity or flat receiver. The optical efficiency of this system is obtained through the integration of the local optical efficiency of each reflecting point in the whole reflecting area. The effect of directional characteristics of concentrated energy on the focal plane is also considered by the angular dependent model. With Gaussian and polynomial model of effective brightness distribution, the system efficiency can be calculated quickly and precisely. The size of receiver and rim angle of dish are optimized to maximize the annual net thermal energy which is collected at different optical errors, and heat loss coefficients. The results show that it will give better prediction to the performance of the paraboloidal dish with a windowed-cavity receiver or flat receiver, and the optimal rim angle will decrease when the effects of the incidence angle are considered in the model. If the optical error is less than 4 mrad, a non-window cavity receiver is preferred and the optimal geometric concentration ratio will be over 3000; if the optical error is large than 4 mrad, a windowed-cavity receiver is preferred, with an optimal geometric concentration of less than 1200. (C) 2013 Elsevier Ltd. All rights reserved.