In this research, the effect of break in a composite material containing one fibre with non-uniform cross section area was investigated depending on Nearest Neighboring Load Theory. Using Shear Lag Theory, a new equation described the redistribution phenomena was derived starting from the Beyerlein and Landis s equation that deals with the redistribution phenomena in a uniform fiber composite material. A mathematical model described the redistribution stresses phenomena in normal stress due to break in non-uniform fiber of composite material was made. Also, the finite elements model was built using ANSYS 11.0 software.A set of numerical calculating was done in order to study the parameters (Width of the matrix and diameter of the fibre )affecting on the normal stress values and to verify the new equation. The comparison between the ANSYS results and new equation results was done and a good agreement was found.