The problem of vibration isolation of a device installed on four three-degree elastic shock absorbers with nonlinear characteristics, as an example of vibration isolation of a discrete system of arbitrary structure with several nonlinear elastic shock absorbers is considered in given paper. An analytical description of mechanical models is applied According to this description a special computer algebra system KiDyM (SCAS KiDyM) constructs differential equations of motion, linearizes inertial and elastic terms by means of elimination of the first small terms, carrying out harmonic linearization of the second one. After getting linear multi-mass mathematical model, the KiDyM software package performs calculations of free vibrations and presents the results in the form of skeletal curves. It allows to determine their sensitivity to the values of elastic and inertial parameters, It makes possible to carry out a cycle of calculations with varying model parameters to achieve optimal characteristics of the vibration protection system by shear and deformation of skeletal curves. An example of the problem analysis solution to the above-mentioned vibration protection system of a device performing spatial vibrations is given. Thus, the system contains 12 nonlinearities. The method for determining the experimental elastic characteristics for specimens of two types of shock absorbers is described. The possibilities of narrowing the spectrum of free vibrations by taking into account the nonlinearity of shock absorbers and the problem of skeletal curves construction of systems with several nonlinearities with generalized coordinates as the main coordinates of the oscillatory system.