In unidirectional composite laminates, when there is a slight deviation between fiber and load-applying direction, the failure mode in tensile and compression will be changed from fiber breakage and buckling, respectively, and will be turned to matrix cracking. The transient angle is the angle of misalignment between fiber and load-applying direction, in which the strength properties of the composite will sharply and considerably decrease due to the change of failure mode. In this paper, the transient angle has been investigated experimentally in fiber-reinforced glass epoxy unidirectional composites. To determine the transient angle, certain unidirectional composite specimens with specific digression angles from the load-applying direction were manufactured due to standards, and tensile and compression tests were performed on them. Results demonstrate that the tensile transient angle is between 4° and 8°, and the compressive transient angle is between 8° and 12°. Moreover, experimental results were compared with analytical calculations using Hashin’s failure criteria. Investigations showed that Hashin failure criteria can adequately predict the amount of load causing failure in unidirectional composite laminates before the transient angle. Still, by approaching this angle, Hashin’s failure criteria can’t correctly predict the load causing failure, and error will increase gradually as it passes the transient angle. This error will occur after the transient angle because Hashin’s Failure Criteria can’t predict changes in failure modes in unidirectional composite laminates.