In the recent years, it has been established that b/h or h/b (b = length of the structure in the lateral direction and h = approach flow depth) is the dominant factor for the estimation of local scour depth around abutments and piers. One of the major limitations of the Lacey formula is that it predicts only one value of the scour depth for a specific river because of the absence of important parameters b and h. Therefore, its application is quite uncertain for variable b and h. Considering its limitations and experimental facts of flow concentration and shear stress amplification close to above structures, the original Lacey formula is modified introducing the parameters b and h. The applicability of the original as well as modified Lacey formula is tested to the data collected from major rivers in Bangladesh.