Abstract. We study, both analytically and numerically, the behavior of magnetic pressure and density fluctuations in turbulent isothermal magnetohydrodynamic (MHD) flows in a slab geometry. We first consider "simple" MHD waves, which are the nonlinear analogue of the slow, fast and Alfvén linear waves, and show that the dependence of magnetic field strength B on density ρ in a simple wave depends on the mode which is considered: for the slow mode, B 2 c 1 − c 2 ρ, while for the fast mode, B 2 ρ 2 . We also perform a perturbative analysis about a circularly-polarized plane Alfvén wave to investigate Alfvén wave pressure, recovering the results of McKee and Zweibel that B 2 ρ γe , with γ e 2 at large M a , γ e 3/2 at moderate M a and long wavelengths, and γ e 1/2 at low M a . This wide variety of behaviors implies that a single polytropic description of magnetic pressure is not possible in general, but instead depends on which mode dominates the density fluctuation production. This in turn depends on the angle θ between the magnetic field and the direction of wave propagation and on the Alfvénic Mach number M a . Typically, at small M a , the slow mode dominates, and B is anticorrelated with ρ. At large M a , both modes contribute to density fluctuation production, and the magnetic pressure decorrelates from density, exhibiting a large scatter, which however decreases towards higher densities. In this case, magnetic "pressure" does not act as a restoring force, but rather as a random forcing. These results have implications for the probability density function (PDF) of mass density. The nonsystematic behavior of the magnetic pressure causes the PDF to maintain the log-normal shape corresponding to non-magnetic isothermal turbulence, except in cases where the slow mode dominates, in which the PDF develops an excess at low densities because the magnetic "random forcing" becomes density-dependent. Our results are consistent with the low values and apparent lack of correlation between the magnetic field strength and density in surveys of the lower-density molecular gas, and also with the recorrelation apparently seen at higher densities, if the Alfvénic Mach number is relatively large there.