Significant variation can be found in measurements for the longitudinal tensile strength of the same unidirectional (UD) composite. A splitting failure is one of the main reasons. It is shown in this paper that the shear stress component resulted from a longitudinal tension and a fiber misalignment can cause the matrix to fail before fiber break. The misalignment angle consists of an initial off‐axial angle and a further fiber rotation during the loading. Based on the micromechanics Bridging Model and the matrix true stress theory established by the author, splitting failure has been analyzed and predicted rigorously in this paper, only using the fiber and matrix properties together with the fiber misalignment angle. The fiber initial misalignment angle of a unidirectional plate can be obtained from testing statistics, or deducing from measured longitudinal compression strength. Our research indicates that the longitudinal tensile strength and the relevant failure mode can be significantly affected by the fiber initial misalignment. An easily ignored failure mode and relative mechanical analysis of a composite under longitudinal tension are given. Such a failure is caused by matrix tension‐shear failure due to an unavoidable fiber misalignment. It has been found that the tension strengths are very sensitive to fiber initial misalignment angle.