A heatsink mounting system (10) is provided for containing and engaging a heatsink (16) against a heat generating component, typically an IC chip (18). The system (10) is includes a rectangular integrally formed resilient frame (12) defining a cavity (26) in which the heatsink (16) is contained. The frame (12) includes a pair of opposed lateral sides (30) and a pair of opposing gripping sides (28) with L-shaped corner blocks (32) depending from the intersections thereof. The gripping sides (28) include centrally positioned grip handles (38) with curved handle posts (39) extending upward and grip blocks (34) depending therefrom, each grip block (34) having a grip tongue (36) at the lower extent thereof extending inward into the cavity (26). Inward pressure on the grip handles (38) forces the grip tongues (36) outward to release objects captured thereby.