The invention relates to a flexible orifice for pop-up style dispensing with a wet wipes dispenser. The orifice includes a flexible, rubber-like sheet having a top surface and a bottom surface. A continuous slit extends across the top and bottom surfaces of the sheet and enables a wet wipe to pass from the bottom surface to the top surface or from the top surface to the bottom surface. The continuous slit has at least one curved portion connected with at least one non-curved portion. Alternately, the continuous slit has at least one zigzag portion connected with a pair of end leg portions.