Resonance in a driven two-level system: Analytical results without the rotating wave approximation

► We consider a two-level system driven by the cnoidal time-dependent field. ► Scheme for constructing the exact analytic solutions of the time-dependent Schrödinger equation. ► Effective analytic approximation of the problem with linearly polarized harmonic wave. ► Resonance conditions in the analytic form, including the Bloch-Siegert shift.