In this paper we will give the method of construction of cyclic incomplete block designs for v treatments in blocks of size k, where v ≤18. r ≤ 20 and k ≤ v-2. We will consider only Regular Graph (R.G.) designs. All the designs for r > 10 are new and many other new designs for r ≤ 10 are also given. In this paper we give designs for two representative cases i.e. v = 6 and 8. k = 4 and r ≤ 20. The full set of designs can be obtained from the first named author.