The dielectrophoretic forces acting on and the resulting velocities of cylindrical and spherical particles embedded in perfectly dielectric viscous fluids are calculated analytically. The fluids are confined in cylindrical/spherical shells and in semi-infinite media with prescribed potential distributions along the surfaces of the media. The forces are calculated by evaluating the Maxwell stress tensor. The velocities of the particles are obtained by solving the Stokes equation for creeping flow. The range of validity of force calculations based on the dipole-moment approximation is estimated.