Experimental design, used to study the effect of some factors on a process, have wide application in modern scientific research. Main purpose of this research project is the study and construction of complete diallel cross (CDC) design and partial diallel cross (PDC)design by method of cyclic shifts. Diallel cross designs for block designs were developed by different authors. Schmidt (1919) first introduced “the Diallel Cross Design”. Following the main structure of diallel cross deigns, a new designs for different classes of designs are constructed by method of cyclic shifts. This technique is useful to establish several series construction plans. Optimality and efficiency of different classes of designs are also obtained in this project. Uddin and Morgan (1990) derive a general construction technique for specific classes of balanced incomplete block designs with nested rows, which impose more restriction on parameters. A general balanced incomplete block designs with nested rows and columns construction technique is derived by Shaffer and Srivastav(2009). The universal optimality of all designs arising from the construction techniques is also obtained. In this thesis, we are followed the proposed model (for unblocked situation) of Ghosh and Das (2003), we have constructed CDC and PDC design using a new method called cyclic shifts. The significant aspect of method of cyclic shifts is that the properties of a design can be obtained from the off-diagonal elements of the concurrence matrix without constructing the actual blocks of the design. The newly proposed designs possess the property of A-optimality for some specific values of v, b and block size.