The orthotropic bimaterial antiplane interface end of a flat lap is studied by constructing new stress functions and using the composite complex function method of material fracture. The expressions of stress fields, displacements fields and the stress intensity factor around the flat lap interface end are derived by solving a class of generalized bi-harmonic equations. The result shows that this type of problem has one singularity, the stress field has no singularity when two materials have constant ratio Γ > 0, the stress field has power singularity, and the singularity index has a trend to −1/2 as Γ increases. The derived equation is verified with FEM analysis.