Flexible intelligent metasurface (FIM) technology holds immense potential for increasing the spectral efficiency and energy efficiency of wireless networks. In contrast to traditional rigid reconfigurable intelligent surfaces (RIS), an FIM consists of an array of elements, each capable of independently tuning electromagnetic signals, while flexibly adjusting its position along the direction perpendicular to the surface. In contrast to traditional rigid metasurfaces, FIM is capable of morphing its surface shape to attain better channel conditions. In this paper, we investigate the single-input single-output (SISO) and multiple-input single-output (MISO) communication systems aided by a transmissive FIM. In the SISO scenario, we jointly optimize the FIM phase shift matrix and surface shape to maximize the end-to-end channel gain. First, we derive the optimal phase-shift matrix for each tentative FIM surface shape to decompose the high-dimensional non-convex optimization problem into multiple one-dimensional subproblems. Then, we utilize the particle swarm optimization (PSO) algorithm and the multi-interval gradient descent (MIGD) method for updating the FIM's surface shape to maximize the channel gain. In the MISO scenario, we jointly optimize the transmit beamforming, the FIM surface shape, and the phase shift matrix to maximize the channel gain. To tackle this complex problem with multiple highly coupled variables, an efficient alternating optimization algorithm is proposed. Simulation results demonstrate that FIM significantly improves channel gain compared to traditional RIS and exhibits good adaptability to multipath channels.