Methods of increasing the bearing capacity of corrugated metal structures of transport constructions using transversal stiffening ribs in the form of additional corrugation and stiffeners are given. Based on the theory of elasticity, a mathematical model for estimating the stress-strain state of transport constructions made of corrugated metal structures reinforced with stiffening ribs in the form of double corrugation was developed. The method of determining equivalent forces during rolling stock passage is offered. It has been established that double corrugation increases the bearing capacity of corrugated metal structures. Therefore, additional corrugation of corrugated metal structures reduces stresses by up to 20% and deflections by 50%. The obtained results show that the increase in rolling stock speed does not lead to a significant increase in stresses and strains in CMS when the railway track corresponds to the design state.