Elastic optical networks could increase the sprectrum usage ratio greatly and provide users with flexible bandwidth granularity compared to the traditional wavelength division multiplexing networks. To improve the existing algorithms of routing and spectrum assignment in EONs, An integer linear programming model was set up to formulate the Routing and Spectrum Assignment problem, and two heuristic algorithms were proposed, which combine the traffic grooming with most solts first and longest path first, respectively, thereby increasing the spectrum resource utilization further. The reordering rule and procedure of the proposed algorithms were designed. The expermients under the smallsize network (6node simple network), mediumsize network (14node NSFNET) and largesize network (19node telecommunication backbone network) show that the proposed algorithms could increase the spectrum resource utilization effectively when compared with existing algorithms.