Reconfigurable intelligent surfaces enhance wireless systems by reshaping propagation environments. However, dynamic metasurfaces (MSs) with numerous phase-shift elements incur undesired control and hardware costs. In contrast, static MSs (SMSs), configured with static phase shifts pre-designed for specific communication demands, offer a cost-effective alternative by eliminating element-wise tuning. Nevertheless, SMSs typically support a single beam pattern with limited flexibility. In this paper, we propose a novel Movable Intelligent Surface (MIS) technology that enables dynamic beamforming while maintaining static phase shifts. Specifically, we design a MIS architecture comprising two closely stacked transmissive MSs: a larger fixed-position MS 1 and a smaller movable MS 2. By differentially shifting MS 2's position relative to MS 1, the MIS synthesizes distinct beam patterns. Then, we model the interaction between MS 2 and MS 1 using binary selection matrices and padding vectors and formulate a new optimization problem that jointly designs the MIS phase shifts and selects shifting positions for worst-case signal-to-noise ratio maximization. This position selection, equal to beam pattern scheduling, offers a new degree of freedom for RIS-aided systems. To solve the intractable problem, we develop an efficient algorithm that handles unit-modulus and binary constraints and employs manifold optimization methods. Finally, extensive validation results are provided. We implement a MIS prototype and perform proof-of-concept experiments, demonstrating the MIS's ability to synthesize desired beam patterns that achieve one-dimensional beam steering. Numerical results show that by introducing MS 2 with a few elements, MIS effectively offers beamforming flexibility for significantly improved performance. We also draw insights into the optimal MIS configuration and element allocation strategy.