This paper presents some examples of "multidimensional incomplete block designs," a class of designs introduced as such by Potthoff [2] to provide analogues for the familiar two-factor incomplete block design. Much of the content of [2] was subsequently presented in [3], [4], [5], and [6]. Three-dimensional incomplete block ("3DIB") designs and four-dimensional incomplete block ("4DIB") designs for additive models are discussed in general terms in [3] and [4] respectively; our purpose in this paper will be to provide examples to which the tools developed in [3] and [4] can be applied. The original results of this paper have been presented in [1].