An improved no-spill cup construction and valve assembly. When not in use, an opening in the flexible material rests against a blocking element, sealing off the opening against the flow of liquid. The closed position provides an extremely secure seal against fluid leakage, such that inadvertent spills, such as by turning the cup upside down, are ineffective. The act of sucking at the cup spout creates negative pressure or a partial vacuum against the flexible material, lifting the opening off of the blocking element, and unblocking that opening. When the opening is unblocked, liquid can flow freely through the valve and spout.