Abstract: During the drilling process of deep and ultra-deep wells, the high downhole temperature and the large tensile force on the drilling tools in the well lead to a large error in the measurement of well depth with drilling. For this reason, considering the influence of the internal temperature, thermal expansion coefficient, axial force of drilling tools and specifications of drilling tools in different well depths, the drilling tools in the well were segmented at the measurement point, and combined with the results of the downhole temperature measurement with drilling and the analysis of the force of drilling tools in the well, the models of thermal expansion and elasticity tensile correction for the depth measurement with drilling were established, as well as the models for the calculation of the error limits of the thermal expansion correction and the elastic stretching correction and the calculation method of wellbore position uncertainty after correcting thermal expansion and elastic stretching errors of measured depth with drilling were given. Example calculations show that during the drilling of ultra-deep wells, the elongation of drilling tools in the well caused by thermal expansion and elastic stretching can reach more than 10 m. By correcting the thermal expansion and elastic stretching of the measured depth with drilling, the vertical depth errors and the size of the error ellipsoid of the measurement points can be significantly reduced. The results provide a theoretical basis for improving the accuracy of well depth measurement with drilling and scientific calculation of wellbore position uncertainty.