To address the limitations of existing continuum robots in the in-situ inspection of aero-engines, specifically their poor driving capability, low control accuracy, weak load capacity, and insufficient structural stiffness, this article proposes a variable stiffness continuum robot. This design aims to resolve the trade-off between high flexibility and low stiffness, thereby improving control accuracy. Inspired by the environmental characteristics of engine blades and the adsorption mechanism of octopus tentacles, an adsorbable continuum robot composed of multi-segment mortise-and-tenon flexible joints and pneumatic adsorption units connected in series is designed. By actively adhering to the contact environment, the robot achieves structural locking, enhancing its overall stiffness. First, assuming constant curvature, a geometric kinematic model is established to analyze the mapping between bending deformation and structural parameters. Then, with tip deflection as the evaluation criterion, an equivalent stiffness model is formulated based on the Euler-Bernoulli beam theory and the continuity principle. Furthermore, finite element analysis is utilized to simulate the continuum stiffness, investigating the influence of geometric parameters (e.g., the position, quantity, and strength of the adsorption units) to optimize the structural layout. Finally, an experimental platform is established to experimentally analyze and evaluate the proposed structure and the established model. Results show that the equivalent bending stiffness can be regulated from 31.1 N/m in the initial flexible state to 93.3 N/m in the fully adsorbed state. Under the same load, the tip deformation is reduced by 61.3%, achieving an approximate threefold stiffness gain. It verifies the validity of the proposed variable stiffness scheme and the established model.