Filament seals, such as brush seals and leaf seals, are investigated as a potential improved seal for gas turbine applications. As these seals operate in contact with the rotor, a good understanding of their stiffness is required in order to minimize seal wear and degradation. This paper demonstrates that the filament and complete seal stiffness is affected in comparable magnitudes by mechanical and aerodynamic forces. In certain cases, the aerodynamic forces can also lead to an overall negative seal stiffness which may affect stable seal operation. In negative stiffness, the displacement of the seal or rotor into an eccentric position causes a resultant force, which, rather than restoring the rotor to a central position, acts to amplify its displacement. Insight into the forces acting on the seal filaments is gained by investigating a leaf seal, which consists of a pack of thin planar leaves arranged around the rotor, with coverplates on either side of the leaf pack, offset from the pack surfaces. The leaf seal is chosen due to its geometry being more suitable for analysis compared to alternative filament seals such as the brush seal. Data from two experimental campaigns are presented which show a seal exhibiting negative stiffness and a seal exhibiting a stiffness reduction due to aerodynamic effects. An empirical model for the forces acting on leaf filaments is developed based on the experimental data, which allows separation of mechanical and aerodynamic forces. In addition a numerical model is developed to analyze the flow approaching the leaf pack and the interleaf flow, which gives an insight into the causes of the aerodynamic forces. Using the empirical and numerical models together, a full picture of the forces affecting leaf stiffness is created. Validation of the models is achieved by successfully predicting seal stiffness for a further data set across the full range of operating conditions. The understanding of aerodynamic forces and their impact on filament and seal stiffness allows for their consideration in leaf seal design. A qualitative assessment of how they may be used to improve seal operation in filament seals is given.