Keywords:Beam on elastic foundation, partial damage to the foundation, sudden structural changes, transient dynamic processes, the dynamic increments of strain and stress. Abstract. One of the major problems of modern structural mechanics is sensitivity analysis of actual and projected designs to various effects not provided for under normal operating conditions, arising in particular in emergency situations, as a result of wear and damage accumulation, etc. The paper presents a physical and mathematical model of the transient dynamical processes initiated in a beam on an elastic foundation with a sudden partial or fully destruction of the foundation. Mathematical models are the differential equations of the static bending of initial and damaged beam, equations of the free and forced vibrations of sections beams formed after damage foundation, with the initial and boundary conditions
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