he issues of formalization and numerical solution of the problems of calculating tolerances for the parameters of corrective elements for a linear induction acceleration system, which are directly related to the performance of a real object, are considered. The key moments of the dynamics of the transverse motion of particles for a specific structure of a linear induction system of acceleration are studied for given values of energy for each of the periods of the resonator. The presence of parasitic electric and magnetic fields, which arise as a result of particle displacement relative to the accelerator axis and change the transverse components of the pulses, is taken into account. The original difference model of the induction system has been transformed into a linear form. To formulate the problem statements for calculating tolerances, the scatter vectors of phase coordinates and tolerances for the correction parameters are introduced. In order to apply the methods of practical stability, the set of tolerances for the parameters of the corrective elements is given in the form of an ellipsoid. Provided that the initial displacements of the transverse coordinates relative to the axis of the accelerator are known constant values, the structured tolerance region was estimated under known linear restrictions on the spread of the phase coordinate vectors. Due to the developed algorithms of practical stability, the original problem of calculating tolerances is reduced to the problem of finding the maximum of a linear form on an ellipsoid. Some important types of restrictions on deviations of phase coordinates concerning the estimation of tolerances on the parameters of the first correction element and the number of particles are investigated. For the case of non-linear dynamic constraints on the spread of the phase coordinate vector, it is proposed to approximate the convex closed set by tangent hyperplanes. From the standpoint of practical stability, the problem of estimating tolerances for the case of given restrictions on the spread of the quality criterion is considered. With the help of practical directional stability algorithms, it is proposed to estimate the maximum tolerance ranges for parameters in terms of volume in the presence of dynamic restrictions on the spread of phase coordinates or a quality criterion.