Two-dimensional indium selenide (InSe) has attracted extensive attention recently due to its record-high charge carrier mobility and photoresponsivity in the fields of electronics and optoelectronics. Nevertheless, the mechanical properties of this material in the ultra-thin regime have not been investigated yet. Here, we present our efforts to determine the Young's modulus of thin InSe (∼1-2 layers to ∼34 layers) flakes experimentally by using a buckling-based methodology. We find that the Young's modulus has a value of 23.1 ± 5.2 GPa, one of the lowest values reported to date for crystalline two-dimensional materials. This superior flexibility can be very attractive for different applications, such as strain engineering and flexible electronics.