Analytical expressions for limiting flux, limiting concentration at the membrane surface, limiting operating pressure are developed for osmotic pressure controlled cross flow ultrafiltration. Modified Sherwood number relationships incorporating the effects of suction and variations of physical properties are used to estimate mass transfer coefficient in a rectangular geometry. The model is solved to predict the limiting flux of bovine serum albumin and dextran data, obtained from the literature. A parametric study of limiting flux with different parameters (e.g., Reynolds number, feed concentration, real retention of the membrane, etc.) is also carried out. Further, the analysis is also carried out for a partially retentive membrane. Explicit quantification of limiting pressure would be of immense help for the design engineers from both operational and economic points of view.