With the advancement in oil exploration, producible oil and gas are being found in low resistivity reservoirs, which may otherwise be erroneously thought as water zones from their resistivity. However, the evaluation of low resistivity reservoirs remains difficult from log interpretation. Since low resistivity in hydrocarbon bearing sands can be caused by dispersed clay, laminated shale, conductive matrix grains, microscopic capillary pores and high saline water, a new resistivity model is required for more accurate hydrocarbon saturation prediction for low resistivity formations. Herein, a generalized effective medium resistivity model has been proposed for low resistivity reservoirs, based on experimental measurements on artificial low resistivity shaly sand samples, symmetrical anisotropic effective medium theory for resistivity interpretations, and geneses and conductance mechanisms of low resistivity reservoirs. By analyzing effects of some factors on the proposed model, we show theoretically the model can describe conductance mechanisms of low resistivity reservoirs with five geneses. Also, shale distribution largely affects water saturation predicted by the model. Resistivity index decreases as fraction and conductivity of laminated shale, or fraction of dispersed clay, or conductivity of rock matrix grains increases. Resistivity index decreases as matrix percolation exponent, or percolation rate of capillary bound water increases, and as percolation exponent of capillary bound water, or matrix percolation rate, or free water percolation rate decreases. Rock sample data from low resistivity reservoirs with different geneses and interpretation results for log data show that the proposed model can be applied in low resistivity reservoirs containing high salinity water, dispersed clay, microscopic capillary pores, laminated shale and conductive matrix grains, and thus is considered as a generalized resistivity model for low resistivity reservoir evaluation.