  In the end of the 19th century Bricard discovered a phenomenon of flexible
polyhedra, that is, polyhedra with rigid faces and hinges at edges that admit
non-trivial flexes. One of the most important results in this field is a
theorem of Sabitov asserting that the volume of a flexible polyhedron is
constant during the flexion. In this paper we study flexible polyhedral
surfaces in the 3-space two-periodic with respect to translations by two
non-colinear vectors that can vary continuously during the flexion. The main
result is that the period lattice of a flexible two-periodic surface
homeomorphic to a plane cannot have two degrees of freedom.
