The theory of the Brownian motion of deformable particles is presented taking into account the interaction between the rotational motion of the particle and vibrations of its form. The changes of the form of the Brownian particle are described by means of the coordinates used in the collective model of the atomic nuclei. The Einstein-Smoluchowski kinetic equation has been obtained in these coordinates. A canonical transformation of the variables is carried out into the space of the Eulerian angles and two deformation parameters. An approximate solution of the kinetic equation has been found using the new variables for particles which have an axially symmetrical shape in equilibrium. Simple time correlation functions of dynamic variables of the particle are calculated.
