This article presents a mixed lubrication model for point contacts with considering the inlet starvation and interasperity cavitations. The pressure distribution on the entire computational domain is obtained through solving a unified Reynolds equation system without identifying hydrodynamic or asperity contact regions. The Jacobsson-Floberg-Olsson mass-conservative boundary conditions are incorporated in the lubrication analysis based on Elrod's algorithm. The inlet oil supply condition which may bring about starvation and local cavitation phenomenon is considered by defining the inlet lubricant thickness distribution. The fast Fourier transform based technique is employed to speed up the surface deformation calculation. A unique solution scheme is constructed to solve full film region, cavitation region, and contact region simultaneously. The model has been applied to the lubrication problems of textured surface under starved conditions. Numerical examples are analyzed and the results show that the present model can be used to investigate the lubrication performance under starved conditions, and that the solution methods are computationally efficient and robust.