HIV-1 infection requires passage of the viral core through the nuclear pore of the cell, a process that depends on functions of the viral capsid. Recent studies have shown that HIV-1 cores enter the nucleus prior to capsid disassembly. Interactions with the nuclear pore complex are 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 property is linked to nuclear entry and infectivity. Using atomic force microscopy-based approaches, we found that purified wild type cores rapidly returned to their normal conical morphology following a severe compression. Results from independently performed molecular dynamic simulations of the mature HIV-1 capsid also revealed its elastic property. Analysis of four HIV-1 capsid mutants that exhibit impaired nuclear entry revealed that the mutant viral cores are brittle. Suppressors of the mutants restored elasticity and rescued infectivity and nuclear entry. Elasticity was also reduced by treatment of cores with the capsid-targeting compound PF74 and the antiviral drug lenacapavir. 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.