In Section 2 we have defined the Kronecker product of matrices. This definition and some properties of the Kronecker product of matrices are given in [1]. Section 3 is devoted to a general discussion of an application of the concept of the Kronecker product of matrices to define the Krnoecker product of designs. This section also contains two theorems which illustrate the use of the method of obtaining Kronecker products of designs. Definitions of some well-known designs are given in Section 4, which also contains a number of results giving explicit forms of certain Kronecker products. Finally some illustrations of a few results of Section 4 are given in Section 5.