Numerical simulations of the elastohydrodynamic lubrication (EHL) have been conducted by many researchers, in which the entrainment velocity is usually parallel to one of the axes of Hertzian contact ellipse. However, in some engineering applications, such as the counterformal contacts in spiral bevel and hypoid gears, entraining velocity vector may have an oblique angle that could possibly influence the lubrication characteristics significantly. Also, a vast majority of gears operate in mixed EHL mode in which the rough surface asperity contacts and lubricant films coexist. These gears are key elements widely used for transmitting significant power in various types of vehicles and engineering machinery. Therefore, model development for the mixed EHL in elliptical contacts with an arbitrary entrainment angle is of great importance. In the present paper, a recently developed mixed EHL model is modified to consider the effect of arbitrary entraining velocity angle, and the model is validated by comparing its results with available experimental data and previous numerical analyses found in literature. Based on this, numerical simulations are conducted to systematically study the influence of entrainment angle on lubricant film thickness in wide ranges of speed, load, and contact ellipticity. The obtained results cover the entire lubrication spectrum from thick-film and thin-film lubrication all the way down to mixed and boundary lubrication. In addition, minimum film thickness prediction formula is also developed through curve-fitting of the numerical results.