Stereo image super-resolution (SSR) aims to enhance high-resolution details by leveraging information from stereo image pairs. However, existing stereo super-resolution (SSR) upsampling methods (e.g., pixel shuffle) often overlook cross-view geometric consistency and are limited to fixed-scale upsampling. The key issue is that previous upsampling methods use convolution to independently process deep features of different views, lacking cross-view and non-local information perception, making it difficult to select beneficial information from multi-view scenes adaptively. In this work, we propose Stereo Implicit Neural Representation (StereoINR), which innovatively models stereo image pairs as continuous implicit representations. This continuous representation breaks through the scale limitations, providing a unified solution for arbitrary-scale stereo super-resolution reconstruction of left-right views. Furthermore, by incorporating spatial warping and cross-attention mechanisms, StereoINR enables effective cross-view information fusion and achieves significant improvements in pixel-level geometric consistency. Extensive experiments across multiple datasets show that StereoINR outperforms out-of-training-distribution scale upsampling and matches state-of-the-art SSR methods within training-distribution scales.