The well-known problem of beam–plasma instability acquires new aspects when one or both of the two components (the beam and the plasma) are strongly interacting. We have now theoretically considered the case when the plasma is in the solid phase and forms a lattice. In this situation, the inherent anisotropy of the lattice leads to a coupling between the longitudinal and transverse polarizations. One of the novel features of the beam–plasma instability in this scenario is the possible excitation of transverse modes, which should be an experimentally observable signature of the instability. We have initially concentrated on a 2D toy model with the beam lying in the lattice plane. At the same time, we have initiated a molecular dynamics simulation program for studying various aspects of the penetration of a beam into a plasma lattice. The beam parameters can be adjusted in order to see the effects of increasing coupling strength within the beam and to distinguish between collective phenomena and scattering on individual particles. When both components are strongly interacting, a number of remarkable phenomena—trapping of beam particles, creation of dislocations, local melting of the lattice—may be observed.