We have developed a constrained inversion technique for interpretation of gravity gradient tensor data. For dike and contact models striking in the -direction, the measured and components can be jointly inverted for estimating the model parameters horizontal position, depth to the top, thickness, dip angle, and density contrast. For a given measurement point, the strike direction of the gravity gradient tensor caused by a quasi 2D structure can be estimated from the eigenvector corresponding to the smallest eigenvalue. Then, the measured components can be transformed into the strike coordinate system. It is assumed that the maximum of is approximately located above the causative body. In the case of gridded data, all measurement points enclosed by a square window centered at the maximum of are used to estimate the source parameters. The number of data points used for estimating source parameters is increased by increasing the size of the window. Solutions with the smallest data-fit error were selected as the most reliable solutions from any set of solutions. The gravity gradient tensor data are deconvolved using both dike and contact models within a set of square windows. Then, the model with the smallest data-fit error is chosen as the best model. We studied the effect of random noise and interfering sources using synthetic examples. The method is applied to a gravity gradient tensor data set from the Vredefort impact structure in South Africa. In this particular case, the dike model provides solutions with smaller data-fit errors than the contact model. This supports the idea that in the central dome area there is a predominance of vertical structures related to the formation of the transient crater and subsequent central uplift of the lower and middle crustal material.