The advection of integral lines is an important computational kernel in vector field visualization. We investigate how this kernel can profit from vector (SIMD) extensions in modern CPUs. As a baseline, we formulate a streamline tracing algorithm that facilitates auto-vectorization by an optimizing compiler. We analyze this algorithm and propose two different optimizations. Our results show that particle tracing does not per se benefit from SIMD computation. Based on a careful analysis of the auto-vectorized code, we propose an optimized data access routine and a re-packing scheme which increases average SIMD efficiency. We evaluate our approach on three different, turbulent flow fields. Our optimized approaches increase integration performance up to 5:6 over our baseline measurement. We conclude with a discussion of current limitations and aspects for future work.