A case for a product in a powdery or semi-fluid form includes a rigid body, and a flexible bottom. The rigid body and the flexible bottom define a variable volume compartment for containing the product. The case also includes a fixed screen which is capable of allowing the product to pass during simultaneous pressures on the flexible bottom and on the screen. The product can be a make-up or skin care powder. The flexible bottom can be formed by a flexible membrane, by a piston and/or a foam slab.