Studying the acceleration and propagation mechanisms of Galactic cosmic rays can provide information regarding astrophysical sources, the properties of our Galaxy, and possible exotic sources such as dark matter. To understand cosmic ray acceleration and propagation mechanisms, accurate measurements of different cosmic ray elements over a wide energy range are needed. The PAMELA experiment is a satellite-borne apparatus which allows different cosmic ray species to be identified over background. Measurements of the cosmic ray antiproton flux and the antiproton-to-proton flux ratio from 1.5 GeV to 180 GeV are presented in this thesis, employing the data collected between June 2006 and December 2008. Compared to previous experiments, PAMELA extends the energy range of antiproton measurements and provides significantly higher statistics. During about 800 days of data collection, PAMELA identified approximately 1300 antiprotons including 61 above 31.7 GeV. A dramatic improvement of statistics is evident since only 2 events above 30 GeV are reported by previous experiments. The derived antiproton flux and antiproton-to-proton flux ratio are consistent with previous measurements and generally considered to be produced as secondary products when cosmic ray protons and helium nuclei interact with the interstellar medium. To constrain cosmic ray acceleration and propagation models, the antiproton data measured by PAMELA were further used together with the proton spectrum reported by PAMELA, as well as the B/C data provided by other experiments. Statistical tools were interfaced with the cosmic ray propagation package GALPROP to perform the constraining analyses. Different diffusion models were studied. It was shown in this work that only current PAMELA data, i.e. the antiproton-to-proton ratio and the proton flux, are not able to place strong constraints on propagation parameters. Diffusion models with a linear diffusion coefficient and modified diffusion models with a low energy dependence of the diffusion coefficient were studied in the $\chi^{2}$ study. Uncertainties on the parameters and the goodness of fit of each model were given. Some models are further studied using the Bayesian inference. Posterior means and errors of the parameters base on our prior knowledge on them were obtained in the Bayesian framework. This method also allowed us to understand the correlation between parameters and compare models. Since the B/C ratio used in this analysis is from experiments other than PAMELA, future PAMELA secondary-to-primary ratios (B/C, $^{2}$H/$^{4}$He and $^{3}$He/$^{4}$He) can be used to avoid the data sets inconsistencies between different experiments and to minimize uncertainties on the solar modulation parameters. More robust and tighter constraints are expected. The statistical techniques have been demonstrated useful to constrain models and can be extended to other observations, e.g. electrons, positrons, gamma rays etc. Using these channels, exotic contributions from, for example, dark matter will be further investigated in future. / QC 20120523