Resonant excitation of Alfvén waves by fast particles in a finite pressure plasma in a non-uniform magnetic field is studied. Plasma compressibility in the wave field is determined both by the curvature of the magnetic lines of force and finite Larmor radius of fast particles. A general expression for the instability growth rate is obtained and analyzed; the applicability of the results obtained in the previous paper has also been studied. The finite pressure stabilization of the trapped particles instability has been found. The bounce-resonance effects are analyzed.