A shower pan (10), preferably having rectangular planform includes a central drain (20) that is centered in a floor portion that inclines at a shallow angle (i.e., 3 degrees or so) to front and back sides and opposite ends. The floor portion and includes a shallow channel (46) along the front edge of the shower pan (10) into which all or substantially all water is drained to a second channel (48) into a central drain (20). An apertured grill or cover plate assembly (36) is mounted in the channels and serves as a cover for the various channels. The shower pan (10) is typically installed so that a sill surface (50) is at the same elevation as the pre-existing floor (52) to provide an entry that does not have any type of ‘trip’ points or obstructions that could pose a hazard to the user or impede assistive aids, such as walkers or wheeled chairs.