Numerical simulation of the laminar-turbulent transition in the boundary layer on blunt cones is performed in hypersonic flows by means of WMLES. A sharp cone and two bluntness radii (1.6 and 2.5) mm are considered. The model configuration is similar to the experiment conducted at NASA. The cones are at a zero angle of attack and freestream Mach number, and the interval of unit Reynolds numbers are M_Ḷ = 5.5 and Re = 4.5 × 10⁶ − 8.2 × 10⁷m^-1, respectively. The transition position is determined by means of heat flux with the bluntness radii variation, and the critical Reynolds number is identified from the numerical simulations. A quantitive comparison shows the model is capable of predicting the main features of the boundary layer transition on leading edge bodies. It is expected that the accurate modeling of the boundary layer state of the laminar-turbulent transition can significantly affect the efficiency of the operation of control mechanisms in hypersonic vehicle flights. Namely, the transition line's downstream shift leads to a considerable reduction of the hypersonic vehicle drag.