The fluid antenna concept represents shape-flexible and position-flexible antenna technologies designed to enhance wireless communication applications. In this paper, we apply this concept to reconfigurable intelligent surfaces (RISs), introducing fluid RIS (FRIS), where each tunably reflecting element becomes a fluid element with additional position reconfigurability. This new paradigm is referred to as fluid RIS (FRIS). We investigate an FRIS-programmable wireless channel, where the fluid meta-surface is divided into non-overlapping subareas, each acting as a fluid element that can dynamically adjust both its position and phase shift of the reflected signal. We first analyze the single-user, single-input single-output (SU-SISO) channel, in which a single-antenna transmitter communicates with a single-antenna receiver via an FRIS. The achievable rate is maximized by optimizing the fluid elements using a particle swarm optimization (PSO)- based approach. Next, we extend our analysis to the multi-user, multiple-input single-output (MU-MISO) case, where a multi-antenna base station (BS) transmits individual data streams to multiple single-antenna users via an FRIS. In this case, the joint optimization of the positions and phase shifts of the FRIS element, as well as the BS precoding to maximize the sum-rate is studied. To solve the problem, a combination of techniques including PSO, semi-definite relaxation (SDR), and minimum mean square error (MMSE) is proposed. Numerical results demonstrate that the proposed FRIS approach significantly outperforms conventional RIS configurations in terms of achievable rate performance.