  We investigate Calabi--Yau three folds which are small resolutions of fiber
products of elliptic surfaces with section admitting reduced fibers. We start
by the classification of all fibers that can appear on such varieties. Then, we
find formulas to compute the Hodge numbers of obtained three folds in terms of
the types of singular fibers of the elliptic surfaces. Next we study Kummer
fibrations associated to these fiber products.
