Controlled surface structures have important applications in the fields of flexible electronics, bionic devices, smart materials and surface engineering. Although various instability modes induced by stresses in homogeneous and heterogeneous film systems have been investigated extensively in the past decades, understanding the stress relief mechanisms of gradient film systems is still a challenge. In this work, periodic thickness-gradient metal silver films on flexible polydimethylsiloxane (PDMS) substrates are prepared by using magnetron sputtering technique and by masking weaved copper grid during deposition. The morphological evolutions and structural characteristics of the gradient films in the uniaxial mechanical compression/tension process are detected by using optical microscopy and atomic force microscopy. It is found that the thickness-gradient film spontaneously forms on the PDMS surface due to the specific three-dimensional structure of the weaved copper grid. The maximum film thickness in the mesh center is about twice larger than the minimum one in the region covered by the copper wire. Under the uniaxial mechanical loading, the silver film surface will form stripe wrinkles and straight cracks, which are aligned perpendicular to each other. The variation of film thickness can well modulate the in-plane strain distribution of the film and thus the stress relief patterns. As the compressive strain increases, the wrinkles first form in the region with smaller film thickness, and then extend into the region with larger thickness. The wrinkle wavelength decreases with compressive strain increasing, which is in consistent with the theoretical prediction of accordion model. The wavelength and amplitude of the wrinkles exhibit periodically oscillatory behaviors across the film surface. As the tensile strain increases, the cracks start to propagate in the region with smaller thickness, and then the crack width and number both increase gradually, leading the multiple crack modes to form finally. The crack width and average spacing both increase with film thickness increasing. The morphologies and evolutions of such wrinkles and cracks in the thickness-gradient films are analyzed in depth based on the stress theory. The wrinkle patterns are further simulated by the finite element method, and the simulation results are in good agreement with the experimental results. This study could promote a better understanding of the strain effects of heterogeneous film systems and find the applications in the field of flexible electronics by the structural design of thickness-gradient films.