Abstract: For the solution of the direct and inverse main geodetic problem by the aid of the Gauss-Kruger projection, two questions are concerned; 1). the solution of the geodetic problem on the projecting plane, i.e. the computation of the difference of corrdinates and the direction angle between 2 points by given values of distance and azimuth on ellipsoid; 2). the conversion of the difference of coordinates so obtained to the corresponding geographical positions. Concerning the first question, two methods may be used, i.e. 1). by correcting the direction and distance;2). by Hristow's formulae. In this paper, the second is to be adopted. Further, the author analysing the accuracy of Hristorv's formulae has found out, that if we wish to obtain an accuracy of 0".001, only using terms up to 5th order inclusive, the formulae may be used under 800km. To get more. accurate results, more terms be expanded But, because the terms in these series are products Sⁿ⁺¹/Nⁿ, the longer the distance is, the worse they converge. Hence, using this method to solve geodetic problem the distance is limited, it can used to solve problems not with too long. when S=120km, the 5th order term may be omited, and all the formulae take convenient form. Further, for simplification of computation, the author suggests, to use approximute functions. As for the second question, when the distance(or l)is not long; and the corresponding tables are available the solution is not diffficult:But if S=800km. (or l=9 to 10°);the general formulae are not sufficient. In this paper a simple method by using an auxiliary point annexed has furnished. If auxiliary tables are available, the computation is very convenient, and the amount of computing work is equivalent to the computation of conversion from one zone to another.