The steady‐state, axial plasma confinement by a multiple‐mirror device is studied in the ’’viscous fluid regime,’’ &lgr;/lm≪1 (but not negligible), where &lgr; is the ion‐ion mean‐free‐path andlmis the scale length of magnetic field variations. An approximate analytical solution is obtained by averaging over the rapid variations caused by the individual mirrors and compared to a numerical solution without averaging. A smooth transition is found, with increasing values of &lgr;/lm, from sonic flow to a diffusive flow. Studies are made of the variation in density profiles and confinement times versus &lgr;/lm, mirror ratio, relative mirror width, and number of mirror cells. The viscous fluid regime is found to have the same characteristics as the ideal multiple‐mirror regime for &lgr;/lm→1.