Method for abrasive waterjet cutting of materials determines a constant of cuttability using an abrasive waterjet Kawj, according to version A, where three deformation parameters are measured on a test cut/sample, version B, where two deformation parameters are measured, version C where one parameter is measured, or a version D where the design is carried out by calculating Kawj according to Young's modulus or according to an ultrasonic wave speed of the cut material. This constant is subsequently input to an algorithm. The result of a calculation using the algorithm acquires sufficient numerical and graphical data to an optimum setting of parameters and are generally valid for all engineering materials, and further of data on cut quality, limit depth of cuts and economical parameters, and also on mechanical properties of the cut material with regard to classification of the material into cuttability class.