A linearised model is proposed for the transmission of waves through thin vertical porous barriers, where both the inertial and dominant quadratic drag effects are included. A boundary-value problem is developed in which linear bound- ary conditions holding along the length of the screen are derived from a pair of canonical wave problems, one including an exact geometric description of a slatted screen to determine an inertia coefficient and the other using a quadratic drag law to determine an equivalent linear drag coefficient. The model is then applied to range of wave scattering and sloshing problems involving thin vertical slatted screens in various settings. In each case results are verified by comparison to the solution of a direct nonlinear calculation where the ef- fects of drag have been isolated. We show that the solution to our canonical problem provides a good approximation to the solution of each of the model problems.