By creating a reverse deflection, negative-displacement horizontal well technology can successfully address the issue of construction challenges brought on by too little displacement in front of the horizontal well target. However, conventional horizontal well casing string running models are unsuitable for negative-displacement horizontal wells. This is because conventional horizontal well models assume that the casing string is in contact with the lower side of the borehole, which is inconsistent with the actual situation in negative-displacement horizontal wells. In this study, we examine the effects of fluid viscous resistance and internal and external fluid interaction forces on the running of the casing string using the Gaussian method and the complementary surface equivalence method. Based on the bending beam theory, we establish a deflection model to examine the interaction between the casing string and the borehole wall in the bending section. The friction and hookload calculation models of each well section and the strength check models are also established. The calculation results show that, according to the aforementioned model, there is an average error of 7.5% between the measured data and the calculated frictional force of the H1 and H2 negative-displacement horizontal wells. This error is within the reasonable range of field application and attests to the validity of the theoretical model. Finally, we study the influence of running factors on running ability and strength of casing string using the control variable method. The results indicate that the weight of the casing string is positively correlated with the variation law of the running ability of the casing string, the maximum offset distance and the length of the horizontal section are negatively correlated with the running ability of the casing string, and the borehole curvature is positively correlated with the variation law of the connection stress of the internal and external threads of the casing string. Therefore, in the process of running the casing string in negative-displacement horizontal wells, using heavier casing string and reducing the maximum offset distance and horizontal section length can improve the running ability of the casing string.