The solution of problems of dynamic structure interaction with its base is always connected with a problem of uncertainty of initial information. Most of it concerns the properties of the base. A traditional approach to the solution of problem in such conditions is the probabilistic approach. However, in recent decades other methods are being developed, for example, the theory of possibilities, which allows estimating with incomplete statistics, when the use of probabilistic methods is incorrect. In this paper these methods are used to estimate the outflow of energy from the vibrating structure. The procedure for estimating the impact of different factors on the structure reliability with incomplete or inaccurate initial information is given.