Monitoring of the state of handling equipment structures is a very important task of diagnosing the state of the material of elements of the carrier system of cranes and transporting machines. It is noted that during corrosion, a significant thinning of the walls of structural elements occurs. The safety of crane operation requires this factor to be taken into account. It is proposed to use modern numerical methods for this, i.e. the boundary element method (BEM) and the finite element method (FEM). The implementation of these methods is performed in the Matlab programming and modeling environment (BEM), and the FEM is used in the Ansys package. In accordance with the technologies of these methods, the design diagrams of the lower girders and the crane structure as a whole were formed. Exact models of strain of crane elements during transverse bending and constrained torsion are given. Calculations of the stress-strain state of the crane metal structures have been performed. On the basis of a preliminary field study, a numerical model is proposed for diagnosing the strength and stiffness characteristics of the carrier system of handling equipment using the BEM and FEM, which has never been used in the world.