In recent years, high resolution push broom Linear Array satellite imageries have been attracted world wide attention more than before. This is due to the wealth of the radiometric and geometric information inherent in these images which provide valuable data for environmental analysis, natural disaster forecasting, response and management. However, to employ this technology for the preliminary rapid mapping requires much computational effort. There are basically two main approaches for the geometric correction of Linear Array push broom imageries. These are the so called generic and the rigorous mathematical models. The latter approach incorporates the physical rotations and 3D translations to generate the exterior orientation parameters of each scan line. This is due to the fact that these images have a dynamic geometry in the sense that each image line has its own exterior orientation parameters leading to a multi-projection image. Bearing in mind the narrow angle field of view of the high resolution Linear Array imageries and great number of unknowns in the equations, this approach requires additional auxiliary data for the solution of geometric rectification. The former approach on the other hand employs a rational polynomial function to relate the image and object points. This approach is usually referred to as the rational function model (RFM). However, this method also encounters complications: Fitting flexibility of the rational function model is dependent on the inclusion of the high order polynomial terms. Experimental tests have confirmed that 78 rational polynomials coefficients (RPCs) are quite sufficient for geometric correction of Linear Array imageries. The solution of these RPCs requires a great deal of field works for the measurement of the ground control points. Moreover, to prevent the ill-conditioning of the solution of the Linear equations, regularization and normalization are necessary. Complications of the solution of the RFM may be reduced by employing the direct Linear transformation (DLT) approach. The DLT model is in fact the RFM with only Linear terms. This approach has gained popularity due to its simplicity and requirement for small number of GCPs. Nevertheless, reducing the field work by limiting the number of GCPs is achieved by sacrificing the fitting accuracy of the RFM. The DLT approach is, therefore, unable to produce the optimum solution in the absence of the higher order terms. The accuracy of the DLT solution still further deteriorates in mountainous terrains due to the fact that the DLT model presupposes the relief and tilt displacement to be similar to the single projection frame type images. In this paper a new solution of the DLT model for the geometric handling of the Linear Array imageries is proposed. The proposed approach is based on transferring a Linear Array image into an equivalent virtual single projection image (VSPI). In this way the fitting capability of the classical DLT model when applied to the Linear Array type imageries, particularly in mountainous terrains, can be improved. The reason lies in the fact that the VSPI frame is generated by including the influence of the approximate height information. This makes the relief displacement in the satellite movement direction similar to the relief displacement in the scan line direction. In this paper the fitting defect of the DLT model for the push broom imagery is first proved mathematically. This is then followed by generating the VSPI frames using simulated Linear Array imageries. The space intersection is then applied to the VSPI frame using the DLT model. The simulated study indicates that the fitting accuracy of the DLT can be improved if a VSPI frame is generated using approximate elevation model in a pre-processing stage.