We have recently developed the mass-polariton (MP) theory of light to describe the light propagation in transparent bulk materials [Phys. Rev. A 95, 063850 (2017)]. The MP theory is general as it is based on the covariance principle and the fundamental conservation laws of nature. Therefore, it can be applied also to nonhomogeneous and dispersive materials. In this work, we apply the MP theory of light to describe propagation of light in step-index circular waveguides. We study the eigenmodes of the electric and magnetic fields in a waveguide and use these modes to calculate the optical force density, which is used in the optoelastic continuum dynamics (OCD) to simulate the dynamics of medium atoms in the waveguide. We show that the total momentum and angular momentum in the waveguide are carried by a coupled state of the field and the medium. In particular, we focus in the dynamics of atoms, which has not been covered in previous theories that consider only field dynamics in waveguides. We also study the elastic waves generated in the waveguide during the relaxation following from atomic displacements in the waveguide.