  We present an analytic study of the finite size effects in Sine--Gordon
model, based on the semiclassical quantization of an appropriate kink
background defined on a cylindrical geometry. The quasi--periodic kink is
realized as an elliptic function with its real period related to the size of
the system. The stability equation for the small quantum fluctuations around
this classical background is of Lame' type and the corresponding energy
eigenvalues are selected inside the allowed bands by imposing periodic boundary
conditions. We derive analytical expressions for the ground state and excited
states scaling functions, which provide an explicit description of the flow
between the IR and UV regimes of the model. Finally, the semiclassical form
factors and two-point functions of the basic field and of the energy operator
are obtained, completing the semiclassical quantization of the Sine--Gordon
model on the cylinder.
