In oil and gas (O&G) exploration the well casing, in the form of a long steel tube, maintains the opening of the drilled well hole. Mechanical equipment is often inserted into the well for the purpose of well monitoring, pressure control and various operations. This downhole equipment may be mechanically connected to the pipe casing by the outward radial motion of anchoring teeth such that the inner wall casing is indented. The connection between the tool and the casing must support significant mechanical loads in the longitudinal (axial) direction of the casing, i.e. transverse to the direction of indentation, while minimizing the indentation depth in order to preserve the stiffness and strength of the casing. Consequently, a determination of the ultimate strength of the connection is of critical importance. Failure of this connection involves intense shear of the inner wall of the casing, akin to a machining operation. The critical load for axial slip can be determined experimentally or numerically (or by combination of both). In this study, detailed simulations are performed using the shear-extended GTN (Gurson-Tvergaard-Needleman) model. The choice of model is motivated by the need to accurately the extensive plastic deformation associated with indentation as well as shear-dominated ductile failure on a sub-millimeter scale. The shear-extended GTN model requires a careful calibration of the model parameters by an accurate measurement of the material response. Accordingly, the casing steel was characterized by appropriate measurements under a range of stress states. The calibrated model was used to investigate an idealized two-dimensional representation of the anchoring problem, with a focus on the effect of indentation depth upon connection strength. Both the indentation of the casing inner wall by the anchoring teeth and the subsequent shear of the casing wall were simulated in detail to determine the load required to initiate and progress slip of the anchoring teeth. The results of these analyses show that the connection strength increases linearly with increasing indentation depth.