Development in the field of machining process is based on the use of cooling lubrication fluids which are not harmful to people and environment, and on machining of high added-value products which usually consist of hard-machined materials. That is why cryogenic machining has developed, at which liquefied nitrogen can be used as a cooling lubrication fluid. The PhD thesis explains the design of a cryogenic cutting numerical model which has an ability to predict outputs of the cutting process (temperature, deformations, cutting forces etc.) and surface integrity (residual stresses) after cryogenic machining of Inconel 718. The FEM model in the first research consists of the definition of the values for the surface heat transfer coefficient in dependance to a boundary gaseous nitrogen layer temperature. The experimental results in the second part of the PhD thesis have shown that liquefied nitrogen contributes to better surface integrity because it has a great impact on removing the heat from the cutting zone. The measured cutting forces and residual stresses have validated the numerical model for cryogenic machining and consequently, the FEM model has become an useful tool for planning and optimizing cryogenic machining process.