  We investigate the Casimir effect of a rough membrane within the framework of
the Horava-Lifshitz theory in 2+1 dimensions. Quantum fluctuations are induced
by an anisotropic scalar field subject to Dirichlet boundary conditions. We
implement a coordinate transformation to render the membrane completely flat,
treating the remaining terms associated with roughness as a potential. The
spectrum is obtained through perturbation theory and regularized using the
$\zeta$--function method. We present an explicit example of a membrane with
periodic border. Additionally, we consider the effect of temperature. Our
findings reveal that the Casimir energy and force depend on roughness, the
anisotropic scaling factor and temperature.
