A foundation container having a discharge pump therein, the foundation container comprising: an outer container; a lid hinged to the outer container to be opened and closed vertically; a container main body mounted in the outer container; a pump coupled to an upper center portion of the container main body; and a discharge plate coupled to an upper portion of the pump, and formed with contents discharge holes, wherein the container main body is provided with a ventilation hole formed through a lower portion thereof, a contents container of stretchable material having a space portion for storing contents is inserted in the container main body, and an upper end of the contents container is seated on an upper portion of the container main body to be fixedly coupled by a middle cap coupled to the upper portion of the container main body, such that the contents container is gradually pressed by pumping operation of the pump by elastic pressing action of the discharge plate, so as to discharge the contents to the contents discharge holes of the discharge plate, wherein the contents container is configured such that a lower edge thereof is provided with a rounded curved portion, characterized in that a bottom of the contents container is provided with at least one annular bent portion formed to be bent upward and downward at a position outside a pump accommodating portion of a lower center portion of the middle cap, so as to induce the contents container to be gradually pressed from the rounded curved portion thereof, and the contents container is further provided on an upper bottom surface thereof with spaced protrusions protruding radially to form a gap (t) between the contents container and the outer wall of the pump accommodating portion for discharging the contents from an outer wall surface of the pump accommodating portion of the middle cap when the contents container is pressed and the bottom surface of the contents container is pressed to be brought into close contact with the outer wall surface of the pump accommodating portion of the middle cap, so that the final residual contents are induced to be smoothly discharged. an outer container; a lid hinged to the outer container to be opened and closed vertically; a container main body mounted in the outer container; a pump coupled to an upper center portion of the container main body; and a discharge plate coupled to an upper portion of the pump, and formed with contents discharge holes, wherein the container main body is provided with a ventilation hole formed through a lower portion thereof, a contents container of stretchable material having a space portion for storing contents is inserted in the container main body, and an upper end of the contents container is seated on an upper portion of the container main body to be fixedly coupled by a middle cap coupled to the upper portion of the container main body, such that the contents container is gradually pressed by pumping operation of the pump by elastic pressing action of the discharge plate, so as to discharge the contents to the contents discharge holes of the discharge plate, wherein the contents container is configured such that a lower edge thereof is provided with a rounded curved portion, characterized in that a bottom of the contents container is provided with at least one annular bent portion formed to be bent upward and downward at a position outside a pump accommodating portion of a lower center portion of the middle cap, so as to induce the contents container to be gradually pressed from the rounded curved portion thereof, and the contents container is further provided on an upper bottom surface thereof with spaced protrusions protruding radially to form a gap (t) between the contents container and the outer wall of the pump accommodating portion for discharging the contents from an outer wall surface of the pump accommodating portion of the middle cap when the contents container is pressed and the bottom surface of the contents container is pressed to be brought into close contact with the outer wall surface of the pump accommodating portion of the middle cap, so that the final residual contents are induced to be smoothly discharged.