  In this paper, we study systematically scalar one-loop two-, three-, and
four-point Feynman integrals with complex internal masses. Our analytic results
presented in this report are valid for both real and complex internal masses.
The calculations are then implemented into a {\tt Mathematica} (version $9$)
package and {\tt FORTRAN} program. Our program is cross-checked numerically
with {\tt LoopTools} (version $2.14$) in real as well as complex internal
masses. We find a perfect agreement between our results and {\tt LoopTools} for
all cases. Additionally, this work is applied for evaluating scalar one-loop
Feynman integrals developed leading Landau singularities which may appear in
real scattering processes at colliders. Last but not least, the method used in
this report can also extend to evaluate tensor one-loop integrals. Therefore,
this may open a new approach which can solve the inverse Gram determinant
problem analytically.
