In solid state physics, the combination of an electron and a positively charged hole (absence of electron) is known to play a very important role. Such a combination is called an exciton. It is electrically neutral and can move around and transfer energy like a particle. Excitons are experimentally studied in several branches of physics, such as when dealing with optical lattices, quantum dots and nano-materials. However, such studies have primarily focused on a large number of excitons. The study of a system of a few excitons is still a challenging task for experimentalists. It would be of great interest to present a theoretical study of some aspects of a few-exciton like system, through analytic calculations as well as numerical simulations. Results thus obtained could be relevant to future experimental work. However, this task being difficult it makes sense to start with a simpler model. Therefore, in this project I will focus on the ground state of a few exciton system, where the electrons and the holes are in separate one dimensional (1D) harmonic traps. Using configuration interaction method I obtain numerical results. It is found that, in obtaining the energy spectrum as well as density localization and fermionization, the key parameters are the separation of the traps and the strength of the interaction. I present a comparison of a variety of 1D models, including cases where fermions are replaced by bosons. In this case, short-range contact interactions are used instead of Coulomb interactions. Also, to further understand this system, some bonus has got from dipolar interactions.