Powder bed fusion (PBF) is ideally suited to build complex and near-net-shaped metallic structures such as conformal cooling channel networks in injection molds. However, warpage occurring due to the residual stresses inherent to this process can lead to shape deviation in the internal channels and needs to be minimized. In this research, a novel analytical model based on the Euler-Bernoulli beam bending theory was developed to estimate the residual stress-induced deformation of internal channels printed horizontally using PBF. The model was used to predict the shape deviation for three different shapes of channel cross sections (circular, elliptical, and diamond-shaped), and showed very good agreement with the experimentally determined shapes of nine different internal channels (three cases per cross-sectional shape). Further, the model predictions were used to compensate for the shape deviation in the design stage, resulting in a reduction in root mean square (RMS) deviation of the circular channel by a factor of 2. The proposed approach is thus expected to be a useful tool to generate design-for-AM guidelines for the additive manufacturing of overhangs and internal channels.