A reliability robust design method for multiple failure modes of an ultra-deep well hoisting container, including: defining randomness of a structural parameter, a material property, and a dynamic load of a hoisting container, and solving a random response of a structural failure for a random parameter using a design of experiment method; establishing reliability performance functions of each failure modes in accordance with failure criterion of the hoisting container; establishing a joint probability model of correlated failures using a copula theory in consideration of probability correlation between the failure modes; establishing, a system reliability model with failure correlation of the hoister container; establishing a sensitivity model concerning each random parameter for system reliability of the hoisting container; and establishing, in conjunction with an optimization design model, a reliability robust optimization design model for the hoisting container using a joint failure probability and parameter sensitivity as constraints.