A resiliently deformable container having at least one discharge orifice equipped with a self-sealing dispensing valve, said valve having a resiliently deformable, concave shaped portion with its perimeter sealingly secured across the container's discharge orifice. The self-sealing valve is secured across the orifice so that it is inwardly concave when the container is in an undeformed condition. The concave shaped portion of the valve includes at least one substantially linear slit extending through the thickness of the valve. The valve requires the attainment of a threshold opening pressure to effect inversion from a concave at rest position in order to dispense the package contents. By providing a container with sufficient flexibility to permit manual deformation and sufficient resilience to return substantially to its undeformed configuration when the externally applied forces are removed, a void volume equivalent to the amount of fluid material discharged from the package is provided inside the container after removal of the applied forces. This aids in closing the self-sealing valve which, after venting the container to the atmosphere, returns to an inwardly concave, sealed position until sufficiently large external forces are again applied to the container to effect inversion of the valve and consequent material discharge.
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