Drilling fluids play an important role in the construction of oil and gas wells. Furthermore, drilling of oil and gas wells at offshore fields is an even more complex task that requires application of specialized drilling muds, which are non-Newtonian and complex fluids. With regard to fluid properties, it is necessary to manage the equivalent circulation density because its high values can lead to fracture in the formation, loss of circulation and wellbore instability. Thus, rheology of the used drilling mud has a significant impact on the equivalent circulation density. The aim of the present research is to develop compositions of drilling muds with a low solids load based on salts of formate acid and improve their rheological parameters for wells with a narrow drilling fluid density range. Partially hydrolyzed polyacrylamide of different molecular weights was proposed as a replacement for hydrolized polyacrylamide. The experiment was conducted on a Fann rotary viscometer. The article presents experimentally obtained data of indicators such as plastic viscosity, yield point, nonlinearity index and consistency coefficient. Experimental data were analyzed by the method of approximation. Analysis is performed in order to determine the most suitable rheological model, which describes the investigated fluids’ flow with the least error.