Summary: Balanced incomplete block designs with nested rows and columns (BIBRC) were introduced by M. Singh and A Dey [Biometrika 66, 321-326 (1979; Zbl 0407.62051)]as generalization of the Lattice square designs. The intra-block analysis of these designs has been developed by Singh and Dey. Since the blocks of the BIBRC are incomplete, assuming the block effects as random and row and column classification complete, an attempt has been made in this paper to develop the inter-block analysis of these designs.