Elastic optical networks (EONs) promise to provide high spectrum utilization efficiency due to flexibility in resource allocation. Survivability is regarded as an important aspect of EONs. P-cycle protection is very attractive for EONs due to fast restoration and high protection efficiency. P-cycles have been extensively studied for conventional fixed-grid WDM networks; however, p-cycle design and selection for EONs has received much less attention. In this paper, we consider the design and selection of p-cycles for EONs with distance-dependent modulation. We propose two novel link-based p-cycle evaluation methods: individual p-cycle selection and p-cycle set selection for EONs. Based on these methods, two p-cycle design algorithms, namely, Traffic Independent P-cycle Selection (TIPS) and Traffic-Oriented P-cycle Selection (TOPS), are proposed to find the best set of p-cycles that is able to provide 100% failure-dependent protection against single link failures. We evaluate our algorithms using both static and dynamic traffic models. Simulation results indicate that the proposed algorithms have better performance than commonly used baseline algorithms.