HIV-1 infection requires passage of the reverse transcribing viral core through the nuclear pore of the cell, a process that depends on activities of the viral capsid. Recent studies have challenged the idea that capsid disassembly is required for nuclear entry. Interactions with the nuclear pore complex are apparently necessary but not sufficient for nuclear entry, and the mechanism by which the viral core traverses the comparably sized nuclear pore is unknown. Here we show that the HIV 1 core is highly elastic and that this feature is linked to nuclear entry and infectivity. Using a novel atomic force microscopy-based approach, we found that purified wild type cores return to their normal conical morphology following a severe forced compression. Analysis of two HIV1 mutants that exhibit impaired nuclear entry revealed that the mutant viral cores are brittle. A suppressor mutation reduced brittleness and rescue infectivity. Core elasticity was also reduced by treatment with Lenacapavir, a clinically relevant antiviral drug. Our results indicate that capsid elasticity is a fundamental property of the HIV-1 core that enables its passage through the nuclear pore complex, thereby facilitating infection. These results provide new insights into the mechanisms of HIV-1 nuclear entry and the antiviral mechanisms of HIV-1 capsid inhibitors.