  AIMS: We investigate whether the morphology of bilateral supernova remnants
(BSNRs) observed in the radio band is determined mainly either by a non-uniform
interstellar medium (ISM) or by a non-uniform ambient magnetic field.
  METHODS: We perform 3-D MHD simulations of a spherical SNR shock propagating
through a magnetized ISM. Two cases of shock propagation are considered: 1)
through a gradient of ambient density with a uniform ambient magnetic field; 2)
through a homogeneous medium with a gradient of ambient magnetic field
strength. From the simulations, we synthesize the synchrotron radio emission,
making different assumptions about the details of acceleration and injection of
relativistic electrons.
  RESULTS: We find that asymmetric BSNRs are produced if the line-of-sight is
not aligned with the gradient of ambient plasma density or with the gradient of
ambient magnetic field strength. We derive useful parameters to quantify the
degree of asymmetry of the remnants that may provide a powerful diagnostic of
the microphysics of strong shock waves through the comparison between models
and observations.
  CONCLUSIONS: BSNRs with two radio limbs of different brightness can be
explained if a gradient of ambient density or, most likely, of ambient magnetic
field strength is perpendicular to the radio limbs. BSNRs with converging
similar radio arcs can be explained if the gradient runs between the two arcs.
