Abstract: Two-dimensional Stype profile design can be summed up in solving a binary equations.According to known design parameters of the situation,it can be divided into 21 different unknown numbers combinations.Use dimensionless thought,rewrite the original design.And according to the Angle unknowns equations appeared in equations of position,the equations solving problem merge into four types of problems,every kinds of problem solving method has similarities,which deduced analytical solution under21 different circumstances,the obtained formulas have more concise mathematical form.The dimensionless method combined with trigonometric simplifing in the analytical solution provided a new mathematical model to 2-D profiles designing and is applicable to other types of two-dimensional circular arc profile design problems.Drawing design parameter values range graphics is an important application of analytical solutions,it can make the designer to set unknown parameters reasonably,reduce calculating trial times,improve the design efficiency.The Given the analytical solution of the calculation formula also has certain directive significance for developing the drilling design software.