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Drilling compound hole is very common material processing operation in engineering industry. In this special machining process before drilling the hole the part is rotated about an auxiliary axis parallel to one of the reference axes. Accuracy of the drilled hole is paramount in several applications such as in cylinder head and some other applications of bone surgery. Inaccuracy in hole axis may result in the loss of engine efficiency in the case of Cylinder Head or unsuccessful bone surgery. In the previous papers Murty et al. [8], [9] the algorithms developed had restricted application. In the first paper the tool was restricted to move in vertical plane and WY-plane was considered as reference plane. In the second paper the tool movement was unrestricted in space but the WY-plane was considered as reference plane and the skew error was assumed only in WY-plane.