The Richtmyer-Meshkov instability (RMI) occurs when a shock impulsively accelerates an interface between two different fluids, and it is important in many technological applications such as inertial confinement fusion (ICF) and astrophysical phenomena such as supernova. Here, we present incompressible models of an impulsively accelerated interface separating conducting fluids of different densities in cylindrical geometry. The present study complements earlier investigations on linear and nonlinear simulations of RMI. We investigate the influence of a normal or an azimuthal magnetic field on the growth rate of the interface. This is accomplished by solving the linearized initial value problem using numerical inverse Laplace transform. For a finite normal magnetic field, although the initial growth rate of the interface is unaffected by the presence of the magnetic field, at late-time the growth rate of the interface decays. This occurs by transporting the vorticity by two Alfvén fronts which propagate away from the interface. For the azimuthal magnetic field configuration, the suppression mechanism is associated with the interference of two waves propagating parallel and antiparallel to the interface that transport vorticity and cause the growth rate to oscillate in time with nearly a zero mean value. Comparing the results of the incompressible models with linear compressible MHD simulations show reasonable agreement at early time of simulations.