Choice of dot shape is the most important factors that affect the printing quality in the flexographic printing system. The aim of the operations performed by the machine operator during the printing process (densitometric measurements, ink settings, etc.) is to achieve the same quality from the first printing to last printing. This study attempts to estimate screen density values obtained from the same polymer structure (DFR), 175 Lpi screening and 10 different screen structures using the Artificial Neural Networks method (ANN). Data necessary for calculations were obtained from real values as a result of experimental studies. The correlation coefficient of the data obtained from the model created with ANN for screen density values was found to be 98,902% and this value was found to be consistent with scientific values. According to the results, the neural network model used in flexographic printing systems of different screening methods predictable effect on the printing result.