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Polymer flooding is one of the chemical processes used to enhance the petroleum recovery. The injection of a polymer dissolved in water into a reservoir aims to increase the water viscosity, leading to an improvement of areal and vertical sweep efficiency of the oil that is located inside the pores of the rock formation. The polysaccharides (mainly xanthan gum) and polyacrylamides have been used extensively for this purpose by the oil industry, and several papers were published. However, it is not clear yet how to choose the best polymer for a specific rock formation. In this paper, four polyacrylamides with different structures were evaluated for polymer flooding and the results were correlated to the permeability of the sandstone's core employed. The polyacrylamides of higher average molar mass and higher radius of gyration were more effective in the enhancement of pressure inside the pore rock, especially with the decrease of rock permeability. Even in this case, no evidence of damage by polymer retention or adsorption on the pore rock was shown, indicating that the high polymers selected are good candidates to EOR.