A rheological model conventionally characterizes non-Newtonian drilling fluids. Parameters of the rheological models are estimated by explicitly solving the required number of equations simultaneously. Rheological models are stochastic and this study considers only the deterministic part of the model. Observed data is accepted as arising from randomness due to the system. A nonlinear least squares method is applied to readings of 6 standard Fann viscometer speeds in order to estimate the models' parameters. Forty-five KCl/polymer data sets of varying compositions are prepared. The best-fitting model is chosen according to the box-plot comparison of residual mean squares (RMS) values of 5 candidate mostly used rheological models. The RMS analysis resulted in the Power Law Model to be acceptably defining the behavior of KCl/polymer type drilling fluids. R-2 analysis, which gives only a rough indication, is also performed and observed to support the model selection.