  We derive analytic expressions of the semiclassical energy levels of
Sine-Gordon model in a strip geometry with Dirichlet boundary condition at both
edges. They are obtained by initially selecting the classical backgrounds
relative to the vacuum or to the kink sectors, and then solving the Schodinger
equations (of Lame' type) associated to the stability condition. Explicit
formulas are presented for the classical solutions of both the vacuum and kink
states and for the energy levels at arbitrary values of the size of the system.
Their ultraviolet and infrared limits are also discussed.
