Continual Learning (CL) with foundation models has recently emerged as a promising approach to harnessing the power of pre-trained models for sequential tasks. Existing prompt-based methods generally use a prompt selection mechanism to select relevant prompts aligned with the test query for further processing. However, the success of these methods largely depends on the precision of the selection mechanism, which also raises scalable issues with additional computational overhead as tasks increase. To overcome these issues, we propose a Scalable Low-Rank Adaptation (S-LoRA) method for class incremental learning, which incrementally decouples the learning of the direction and magnitude of LoRA parameters. SLoRA supports efficient inference by employing the last-stage trained model for direct testing without the selection process. Our theoretical and empirical analysis demonstrates that S-LoRA tends to follow a low-loss trajectory that converges to an overlapped low-loss region, resulting in an excellent stability-plasticity trade-off in CL. Furthermore, based on our findings, we develop variants of S-LoRA with further improved scalability. Extensive experiments across multiple CL benchmarks and various foundation models consistently validate the effectiveness of S-LoRA.