The paper formulates and solves the problem of free longitudinal vibration of the lower-limb exoskeleton using the method of Lagrange multipliers. Parts of the exoskeleton were replaced with continuous and discrete elements. The physical model includes properties characterizing the interaction between exoskeleton components, contact with the ground and the method of applying the load. On the basis of the presented model, an algorithm and a computational program were developed. It allowed to

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... uct the studies of the influence of selected model parameters on the longitudinal vibrations of the considered system. topics: discrete-continuous system, exoskeleton, free vibration, Lagrange multiplier formalism