The influence of the acuteness of the model angle and the direction of printing was investigated on different three-dimensional (3D) printers to understand the fidelity of 3D printing. A Polyjet printer and two fused deposition modeling printers were used in the present study. Computer-aided design (CAD) models were designed in the form of a triangular prism with a height of 15 mm and with varying angles of 60A degrees, 45A degrees, 30A degrees, 20A degrees, 10A degrees, and 5A degrees. From the CAD designs, additive manufacturing (AM) models were printed in three different directions by each of the three printers. To investigate the global fidelity of the 3D printers, the height and surface outlines of the AM model cross sections were measured. The fidelity of the AM models with increasingly acute angles was not accurately reproduced when 3D printed, and the surface outlines of the AM model cross sections were different in each direction of printing for each device. Printing technology and printing direction need to be considered if accurate reproduction of acute angles in fine AM structures in medical models is a necessity.