Abstract: The fracture conductivity greatly affects the production capacity of oil gas field. Based on the hexagonal closest packing assumption of proppant, theory of elasticity and Carman-Kozeny formula, a mathematical model of fracture conductivity is established, with taking sand concentration, closure pressure, proppant diameter, proppant material and proppant embedment into account. The result shows that the improved conductivity will achieve with an increased sanding concentration and proppant particle size. The proppant-embedded wall has a very small influence on the conductivity when the pressure is low, and the proppant embedding has a slightly greater influence on the conductivity at high pressure.The calculation model combines the factors affecting the fracture conductivity very well, and provides a theoretical basis for the fracturing development of oil and gas field.