Given three distinct lines (varieties or strains), say A, B and C, we can form three distinct three-way crosses (AB)C, (AC) B and (BC)A. The set of all possible three-way crosses VT = v(v — 1 )(v — 2)/2 among the given set of v lines is termed triallel crosses or a triallel mating design. As the number of lines v increases, the triallel crosses become too many to be accommodated within the resources of the breeder. One of the ways to overcome this situation is to take a sample of three-way crosses, called partial triallel crosses. Estimators for design and genetic components of variance have been developed based on Hinkelmann's model.