Thin film deposition by sputtering is usually performed with projectile-energy-target combinations placing the sputtering mechanism within the linear cascade regime of collisional sputtering. For the purposes of estimating sputter yield values, as well as conveying an understanding of this most important sputtering mechanism, there is a need for an analytical model whose yield expression has a clear and obvious physical meaning, is easy to evaluate with a modest computer, and yet faithfully represents sputtering in this regime. To meet this need, a deliberately simplified model is developed. The yield expression is a product of three terms : the number of recoiling target atoms at the practical endpoint of the cascade, times the probability that they are sufficiently near the surface to escape, and times the probability that they are traveling in the right direction. It is evaluated by calculating (1) the surface binding energy from thermodynamic data, (2) an average energy of the population of target recoils, from their energy distribution at the practical endpoint of a single collision cascade, and (3) an escape probability from the projected ranges of projectile and recoils, based on nuclear energy loss theory. The simplified collisional model reproduces trends in experimental data for the projectile energy-, projectile mass-, and target-dependences of sputter yield.