Shear thickening fluids are smart materials that show a sudden increase in viscosity when exceeding critical shear rates. Different theories have been proposed to explain these properties of shear thickening. The most used of these theories are Order-Disorder Transition and Hydro-Cluster Theory. Due to their reversible properties, shear thickening fluids have been used in many areas. High molecular weight polyethylene glycols showed faster shear thickening fluids behavior. The molecular weight of polyethylene glycol affects many parameters. These parameters are physical bonds, aggregations of molecular, solid particle interactions, and functional groups in the chain. Due to their effect, rheological behaviors of low and high molecular weight polyethylene glycols differ. The mixtures of polyethylene glycols and fumed silica particles show a colloidal distribution. The distribution of fumed silica particle molecules in polyethylene glycol, interaction with each other restriction, and movement of the bulks have affected rheological properties. Physical interactions are manifested in the structure. The mixture showed non-Newtonian behavior in the first and second regions as well. Rheological behaviors of mixtures were compared with experimental data using non-Newtonian models. Power Law, Bingham, Casson, Herschel-Bulkley, and Sisko model equations were used. Silica particle-PEGs mixtures show pseudo plastic in the first region and dilatant fluid behavior in the second region. In the first region, the Power Law model was determined as the most suitable model for experimental data. In the second region, the Herschel-Bulkley model was found to be the most suitable model that was determined by statistical analysis.