The influence of silica nanoparticles on the elasticity of a polymethylmethacrylate (PMMA) melt was investigated. The extrudate swell obtained from the extrusion of the melt through a die and the recoverable deformation after a creep test were measured. As well known from other materials, the extrudate swell becomes smaller by adding fillers, i.e. the elasticity decreases. This is usually explained by the effect of substituting viscoelastic polymer molecules by rigid particles. The linear steady‐state recoverable compliance Je0, however, attains values which are significantly higher than those of the matrix indicating an increase of the elasticity. This effect is postulated to be due to interactions of the matrix molecules with the particle surface giving rise to longer retardation times and higher retardation strengths which lead to larger Je0 according to the theory of linear viscoelasticity. The apparent discrepancy between these two contrary effects is solved by the finding that the recoverable compliance becomes smaller with stress above a critical value and approaches the elasticity of the matrix. This decrease is found in a stress range which is much lower than that applied in the extrudate‐swell experiment. The results of an elastic compliance becoming smaller with stress are interpreted by a detachment of the matrix molecules from the particles.