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A fracture propagation model of radial well fracturing is established based on the finite element-meshless method. The model considers the coupling effect of fracturing fluid flow and rock matrix deformation. The fracture geometries of radial well fracturing are simulated, the induction effect of radial well on the fracture is quantitatively characterized, and the influences of azimuth, horizontal principle stress difference, and reservoir matrix permeability on the fracture geometries are revealed. The radial wells can induce the fractures to extend parallel to their axes when two radial wells in the same layer are fractured. When the radial wells are symmetrically distributed along the direction of the minimum horizontal principle stress with the azimuth greater than 15°, the extrusion effect reduces the fracture length of radial wells. When the radial wells are symmetrically distributed along the direction of the maximum horizontal principal stress, the extrusion increases the fracture length of the radial wells. The fracture geometries are controlled by the rectification of radial borehole, the extrusion between radial wells in the same layer, and the deflection of the maximum horizontal principal stress. When the radial wells are distributed along the minimum horizontal principal stress symmetrically, the fracture length induced by the radial well decreases with the increase of azimuth; in contrast, when the radial wells are distributed along the maximum horizontal principal stress symmetrically, the fracture length induced by the radial well first decreases and then increases with the increase of azimuth. The fracture length induced by the radial well decreases with the increase of horizontal principal stress difference. The increase of rock matrix permeability and pore pressure of the matrix around radial wells makes the inducing effect of the radial well on fractures increase.