Carbonate muds are essential sedimentary components in geological carbon cycles. Model carbonate muds are prepared from crushed, sieved carbonate rock. The carbonate rock particles are primarily smaller than 62.5 µm. Steady-state shear viscosity was measured for model carbonate muds prepared from three types of carbonate rock: limestone Grey, limestone Marl, and limestone Castleton. Model carbonate muds were prepared using fresh water or 3.5 g/L NaCl solution. The carbonate particle concentrations were 1.81 volume percent and 26.95 volume percent, representing semi-dilute and concentrated particle regimes, respectively. Carbonate mud viscosity was measured at temperatures ranging from 8 °C to 35 °C. Shear rates ranged from 60 s−1 to 2500 s−1. Pseudoplasticity occurs at low shear rates and is caused by the release of occluded water during shear-driven breakup and dispersal of particle aggregates. Shear thickening occurs at high shear rates and is caused by transient particle clusters, called hydroclusters, that are reinforced by lubrication forces or frictional particle contacts. Carbonate mud viscosity decreases at increasing temperatures. The presence of 3.5 g/L NaCl in the aqueous phase slightly increased the mud viscosity in the semi-dilute particle concentration regime because of a weak viscosifying effect of NaCl on the aqueous phase. In the concentrated particle regime, electrolytes screened electroviscous effects, reducing the viscosity of muds containing particles with electrically charged surfaces. In aqueous solution, limestone Marl had a comparatively high concentration of charged particles on its surface. Limestone Castleton had a comparatively low concentration of charged particles on its surface. Surface charges were not rheologically evident on limestone Grey.