Elastic Optical Network (EON) architectures are considered as a very promising solution for both huge bandwidth and flexible connection provisioning in next generation optical networks. In EON, a basic problem in network design and operation is the problem of Routing and Spectrum Allocation (RSA). In this article, we focus on offline RSA in a survivable EON scenario with shared backup path protection (SBPP). We formulate RSA/SBPP as an Integer Linear Programming (ILP) problem. Since RSA is a difficult problem itself, we propose several heuristic algorithms including both new proposals called Adaptive Frequency Assignment with Shared Backup Path Protection (AFA/SBPP) and Most Subcarriers and Average Longest Path First (MSALPF) as well as existing RSA methods adapted to the SBPP scenario. We investigate the efficiency of all algorithms for a set of network scenarios and we show that the proposed new algorithms outperform other reference algorithms. Moreover, numerical experiments show that the shared backup path protection approach enables reduction of the spectrum usage up to 28% comparing to the dedicated path protection approach without sharing of backup capacity. However, the difference between these scenarios strongly depends on the network topology and other parameters.