Summary: A scheme for analysis of linear dynamical systems described by stochastic integro-differential equations with non-difference kernels is considered. Such equations are mathematical models of a significant number of phenomena in various scientific and technological fields including the theory of oscillations for objects with lumped and distributed parameters taking into account aero-auto-elasticity, heredity, (thermo)visco-elasticity and aging of materials (asphalt, concrete, biopolymers, rocks, colloidal solutions, composites, natural and synthetic polymers, suspensions, glass, cellulose, etc.) and others. The calculation scheme proposed is based on a modification of the iterative method for approximation of the matrix Green’s function and is designed to compute the first moment functions of the state vector of the system including functions of mathematical expectation and covariance functions. An example shows an application of our scheme for an analysis of a model system with two degrees of freedom.