Abstract: The rational design of two-dimensional (2D) functional materials with targeted mechanical properties remains a significant challenge for emerging device applications, including flexible electronics and micro/nano-electromechanical systems. Conventional high-throughput first-principles screening approaches suffer from high computational costs and limited capability for the inverse design of complex mechanical responses. Because the mechanical behavior of 2D materials is governed by multi-component elastic tensors, whereas existing AI-based generative models mainly rely on scalar property constraints, this work proposes a stiffness-tensor-guided design framework for 2D mechanical functional materials. A diffusion generative model, termed StiGen, is developed by incorporating a stiffness tensor embedding module into the MatterGen framework, using the nine-dimensional Voigt stiffness vector as the generation condition. A classifier-free guidance (CFG) strategy is further introduced to regulate the influence of mechanical targets during inference. Trained on the Computational 2D Materials Database (C2DB), StiGen enables an integrated workflow of crystal structure generation, thermodynamic stability screening, and first-principles elastic-constant validation. The generated structures exhibit controllable mechanical responses under different stiffness tensor conditions. First-principles elastic calculations of 80 candidates demonstrate strong consistency between target and calculated stiffness components, with Pearson correlation coefficients of 0.839, 0.788, 0.705, and 0.660 for C₁₁, C₂₂, C₁₂, and C₆₆, respectively. Further anisotropic and shear response analyses confirm that the model preserves tensorial mechanical information beyond scalar modulus descriptors, enabling component-level regulation of directional stiffness and shear behavior. Among 512 generated structures, 40.8% satisfy the stable-unique-novel (S. U. N.) criteria, indicating reliable structural diversity under targeted mechanical constraints. This work establishes a tensor-conditioned AI framework for the inverse design of mechanical functional materials, providing an effective strategy for discovering novel 2D materials for advanced device applications.