Some properties of the linearized model of the (super)$p$-brane

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.