A new method of constructing a family of resolvable Balanced Incomplete Block designs is given. The design has a hierarchical structure and the sub designs are well known incomplete block designs with good statistical properties. Such designs are useful in industrial applications where blocks are run sequentially. The blocks of the design can be arranged in a row-column array which provides additional measure of classification. Some new properties of Group Divisible designs are given along with some properties of Balanced Block Design. Balanced Block designs with nested rows and columns are introduced. A specialized case of Generalized Group divisible design is discussed. The non-existence theorems and some new methods of construction are given. The analysis of such designs is also given. A new product of matrices called ‘Generalized Kronecker Product’ is introduced and the Hasse-Minkowski invariant of the matrices is obtained. The results are obtained to construct some useful designs. Block Structure properties of Equiblocksized Equireplicated Connected Designs are discussed. A-efficiency of such designs is also obtained.