Recently, stereo image super-resolution (SSR) has achieved impressive performance by leveraging both intra-view and inter-view information. However, existing SSR methods often rely on single-scale features for stereo image feature extraction and overlook multi-dimensional feature interactions, resulting in poor visual quality with unclear and insufficiently sharp reconstruction of details. To address these issues and achieve better performance for stereo image super-resolution, we propose a multi-scale feature cross-dimensional interaction network (MFCINet) for SSR. Specifically, to fully exploit intra-view information, we design multi-scale feature extraction blocks to capture abundant multi-scale texture patterns, including the Local Feature Extraction Block (LFEB), Mesoscale Feature Extraction Block (MFEB), and Global Feature Extraction Block (GFEB). We progressively fuse smaller-scale features with larger-scale features, utilizing the local texture information contained in the smaller-scale features to refine the global structure information of the larger-scale features. To explore richer interactions of complementary features, we introduce the Cross-dimensional Attention Interaction Block (CAIB), which calculates attention between complementary features across different spatial positions and channels, facilitating comprehensive interaction among complementary features across various dimensions. Extensive experiments and ablation studies demonstrate that MFCINet better leverages intra-view and inter-view information to reconstruct clear texture details, achieving competitive results and outperforming state-of-the-art methods.