  We extend a recent formulation of quantum continuum mechanics [J. Tao et. al,
Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a
magnetic field. To accomplish this, we propose a modified Lagrangian approach,
in which motion of infinitesimal volume elements of the system is referred to
the "quantum convective motion" that the magnetic field produces already in the
ground-state of the system. In the linear approximation, this approach results
in a redefinition of the elastic displacement field $\uv$, such that the
particle current $\jv$ contains both an electric displacement and a
magnetization contribution: $\jv=\jv_0+n_0\partial_t \uv+\nabla \times
(\jv_0\times \uv)$, where $n_0$ and $\jv_0$ are the particle density and the
current density of the ground-state and $\partial_t$ is the partial derivative
with respect to time. In terms of this displacement, we formulate an "elastic
approximation" analogous to the one proposed in the absence of magnetic field.
The resulting equation of motion for $\uv$ is expressed in terms of
ground-state properties -- the one-particle density matrix and the two-particle
pair correlation function -- and in this form it neatly generalizes the
equation obtained for vanishing magnetic field.
