Abstarct: Electrostatic interactions between rod-like and stripe-like charged objects play a substantial role in the many systems of condensed matter and soft condensed matter physics such as strongly correlated materials, liquid crystals, electrolytes, polymers and bio-molecules. For example, superconductors and antiferromagnetic Mott insulators are a large class of strongly correlated systems whose quantum phases have been studied intensively. Many results signifying the segregation of charged carriers into fluctuating stripes in cuprate superconductors have been reported. In the ceramic samples La2−xSrxCuO4 co-doped with Nd, the charged stripes are seen by neutron diffraction as a static lattice modulation coherent with low-temperature tetragonal modulation. Nickelates (La2−xSrxNiO4) are the other good empirical realities for observing the charged stripes at low temperatures. The relationship between correlations of charged stripes and high-Tc superconductivity has been studied intensively in nickelates. More physical insights are gained by obtaining a closed-form formula for the interaction of such stripes. Indeed, the closed form gives us much useful information on the physical properties of the system, such as orderings and correlations of the charged stripes and also the thermodynamic properties of the system. Experimental evidence of such interactions is also observed in the colloidal world. Actually, in the colloidal solutions, macromolecules such as DNA molecules, TMV or the fd virus, V2O5 ribbons, crystalline Boehmite (AlOOH) rods, etc, are intrinsically extremely anisotropic and have rod-like and ribbon-like shapes. In the context of an orientational phase transition, it has been elucidated that the electrostatic interaction between the polyelectrolytes leads to a twisting effect which enhances the concentration at the isotropic to nematic (I–N) phase transition. More findings are attained by making use of the form of the interaction energy between such objects. Many efforts have been made to employ the analytical and numerical approaches for computing the electrostatic interaction of two rod-like charged objects. Despite all simulations and analytical approaches, the lack of a closed-form formula for the interaction energy of such anisotropic particles is felt. In this thesis we have obtained a closed-form formula for the interaction energy of two rod like charged objects with lengths 2l1 and 2l2 and arbitrary orientations in three dimensions, separated by r. By using the closed-form formula we have computed the thermodynamic functions of a 1D array of charged rods in which each rod interacts only with two nearest neighbors. Although the electrostatic interaction is long range and there are no practical realizations to vindicate our assumption, one can get more insight about our finding of the closed-form formula and its direct effects on the thermodynamic behavior of a system. Finally the relationship between the behavior of the specific heat and the electrostatic interaction energy is investigated. In the second part of this thesis we have tried to find the electrostatic interaction of two rod-like objects at the presence of screening effects. Actually finding an analytical exxpression for the screened electrostatic interaction of two charged rods is not a trivial task and is conundrum. However, we can obtain useful results by considering a number of axial quadrupole on the rods and investigate their electrostatic interaction for different screening lengths, numerically. The noticeable result is that the orientations with minimum and maximum energies are not changed by adding the screening effects. It means that the presence of any salt cannot change the Min and Max configurations. In the last part of this thesis, we employed our results to discuss the physical properties of the Cuprates. We have studied the structural properties of lightly hole doped cuprates. At lightly doped regions, charge and spin stripes are emerged in different Cu-O laxyers. Considering charge stripes as classical anisotropic objects, we have obtained the orientations of stripes with minimum interaction energy. Our results are in good agreement with the experimental ones. Finally we have concluded that in the lightly doped regime one can neglect the quantum effects and study the physical properties of the system.