Compared with conventional hydraulic fracturing, radial-drilling fracturing presents remarkable advantages and can effectively develop low-permeability reservoirs. The radial borehole can reduce formation fracture pressure and guide the fracture initiation and propagation. Due to the large radial borehole azimuth or the strong anisotropy of the reservoir, the single radial borehole may not efficiently guide the fracture propagation. The researchers proposed multibranched radial-drilling fracturing. However, the research on fracture initiation of multibranched radial-drilling fracturing is inadequate. Radial boreholes usually need certain dip angles to avoid penetrating the interlayer, but the effect of dip angle on the stress field has never been considered before. In this paper, an analytical model for predicting stress distribution around the main wellbore with multiradial boreholes of arbitrary dip angle, azimuth angle, and phase angle is established for the first time, taking full account of the influences of in situ stress, internal pressure, and fracture fluid infiltration on the stress field. The model is utilized to calculate the fracture initiation pressure (FIP) and point out the specific fracture initiation location (FIL). The influences of azimuth angle, dip angle, phase angle, depth difference, and the stress profile radius on fracture initiation pressure, fracture initiation location, and maximum tensile stress distribution are investigated, and a series of sensitivity analyses are carried out. The results show that the areas between the radial boreholes and closer to the walls of radial boreholes are more prone to tensile failure, which provides a theoretical basis for radial boreholes guiding fracture initiation. The reduction of phase angle and depth difference enhances the interference between radial wells, which is conductive to the formation of hydraulic fracture networks between them. As the dip angle increases, the stress becomes increasingly concentrated, and the preferential rock tensile failure becomes increasingly easy. The farther the stress profile is from the main wellbore axis, the smaller it will be influenced by the main wellbore. When the distance exceeds 2R, the maximum tensile stress distribution on the profile remains constant. The research enriches the fracture initiation mechanism of multibranched radial-drilling fracturing and provides guidance for optimizing radial borehole layout parameters of hydraulic fracturing directed by multiradial boreholes.