In situ evaluation of the mechanical properties of existing masonry structures can be a challenging problem because destructive in situ tests are not always feasible. Cohesion and friction coefficients of the mortar-brick interface are fundamental parameters to characterize the shear strength of brick-masonry walls: the slightly invasive in situ test called the “shove test” can be performed to establish rational values for these parameters as described in ASTM C1531, Standard Test Methods for In Situ Measurement of Masonry Mortar Joint Shear Strength Index. During the shove test, a jack pushes one brick of the wall horizontally, while two flatjacks impose a known vertical stress on the masonry portion surrounding the selected unit. In order to insert the horizontal jack and allow the brick to slide, the two adjacent bricks need to be removed, introducing discontinuities within the compression stress flow. At the same time, the service load acting on the pier imposes an additional compressive stress on the bed-joint interface. Moreover, sliding of the test brick would require vertical expansion of the restrained bed joint, resulting in further compression due to dilatancy. Knowing the actual stress distribution after removal of the two bricks and considering the service-load and dilatancy effects are essential to determine the actual compressive stress on the test unit and to derive the correct shear strength parameters from the force applied by the horizontal jack. However, current standards do not address these effects explicitly. The work presented in this paper, validated through in situ and laboratory tests and detailed numerical analyses, consists of an improved methodology for the execution and interpretation of the shove test that estimates the actual compressive stress on the selected brick and consequently provides a more rational interpretation of the shear resistance of the bed joints.