The author uses the method of least squares in cracovian form and second order polynomials for estimating the regional gravity field. Expressions yielding the regional field are obtained very rapidly by using the inverse cracovians of the coefficients as given in the present paper, and there is no need of electronic digital computers for the computation. The equivalent of the entire work done by a computer of this kind in constructing the formula of the regional field, when effected by this method, takes no more than 20 minutes. The method is exemplified by the treatment of two gravity anomalies from the territory of Poland. The author stresses the fact that electronic computers adapted to the use of cracovians and characterized by a very high versatility may be applied in the method.