The HAGIS self-consistent nonlinear wave-particle interaction model. The authors describe the numerical modeling of interaction of energetic particles with a wave possessing a spectrum specific to magnetically confined plasmas in torus thermonuclear reactors. The problem is studied in a coordinate system related to an equilibrium magnetic field whose surfaces are perturbed by a magnetohydrodynamic wave with spectrum of finite amplitude. Particle motion is described by using Hamiltonian formalism. This model of nonlinear wave-particle interaction is self-consistently treated employing a newly developed numerical code HAGIS which does not require a large number of grid points. First, the authors discuss various tests performed on steady problems, and then apply the HAGIS method to examine the kinetic toroidal Alfvén eigenmode instability and to obtain the distribution of alpha-particles in tokamak plasmas. The presented results demonstrate the transition from linear growth regime to a nonlinear saturated state.