The invention discloses a beam structure non-probabilistic reliability solving method capable of considering multi-failure modes. The correlation of two failure models including strength and rigidity is considered; firstly, existing multisource uncertain factors in material characteristics, environment external loading and the like are fully considered, interval mathematics and fuzzy mathematics are adopted to carry out quantization on the multisource uncertain factors and develop propagation analysis; then, the multisource uncertain factors are introduced into a general reliability solving theory, the non-probabilistic reliability solving method is developed, and on the basis of the method, the strength and rigidity reliability degree analysis of a beam structure can be independently carried out; and finally, the correlation of two failure models is comprehensively considered, a correlation constitutive relation equation is established, and the reasonable representation of the correlation among failure modes is realized. The method gives the comprehensive influence on structural strength reliability by different failure modes, can realize the comprehensive optimization design of the structural strength, and guarantees that the design gives consideration to safety and economy.