Many two-factorial experiments are laid out in the designs with split-units. This type of experiment is especially useful in agricultural experiments. A split-plot design and a split-block design are two types of designs with split-units. In this thesis, we consider the optimal properties of some Incomplete Split-Block Designs(ISBDs). A sufficient condition for an ISBD to be universally optimal is given, and the optimal properties for some ISBDs under two linear models (with interaction and without interaction effects) are examined. Some methods of constructing universally optimal ISBD are also given. These construction methods utilize the structure of Balanced Incomplete Block Designs (BIBDs) with respect to both, row and column treatments. In addition, we deal with the linear model considered by Hering and Mejza in which block effects are random variables. We restrict ourselves to the estimation of the elementary contrasts of interaction effects. Two approaches to the analysis of the linear model for observations from an ISBD are considered. The first one is based on the intra-plot stratum in the approach appropriate to multistratum designs. In the second approach, the generalized least square method is used. In both cases, it is shown that the Balanced Incomplete Split-Block Design (BISBD) is universally optimal for the estimation of interaction effects.