  We study the Casimir effect of a membrane embedded in 2+1 dimensions flat
cone generated by a massive particle located at the origin of the coordinate
system. The flat cone is an exact solution of the nonprojectable Horava theory,
similar to general relativity. We consider a scalar field satisfying Dirichlet
boundary conditions, and regularize the spectrum using the $\zeta$--function
technique. In addition, we include the effects of temperature in our analysis.
Our results show that the Casimir force depends on three factors: the
anisotropic scaling z, the mass of the point particle, and the temperature.
