This study presents a model of starved mixed Elastohydrodynamic Lubrication (EHL) in point and line contact to investigate the lubrication performance and material response. In formulating the governing equations for the lubrication, the dimensional Reynolds equation is discretized to involve all possible regimes from the boundary lubrication to fully hydrodynamic lubrication, and an additional algorithm is provided to determine the fractional film content based on the profiles of pressure distribution and film thickness. Solutions of the point contact from the present model are compared with those reported by the previous studies and good consistency can be found. The three-dimensional line contact is used to predict the load carrying capabilities of the film thickness at the interface of mating spur gear teeth. A return mapping method is implemented to take the plastic revolution into account. The solution at the initial stage of a startup process with the lubricant entrainment velocities of  ux = uy = 0 is compared with that from a dry contact to validate the elasto-plastic solutions. Sample cases are presented to reveal the effects of inlet oil supply condition and material plasticity on lubrication starvation.