  Some general properties of the relativistic $p$-dimensional surface imbedded
into $D$-dimensional spacetime and its reduction to the sim\-plest case of the
quadratic Lagrangian (the linearized model) are considered. The solutions of
the equations of motion of the linearized model for the $p$-brane with
arbitrary topology and massless eigenstates, as well as with critical dimension
after quantization are presented. Some generalizations for the supermembrane
are discussed.
