In the finite cell method (FCM), the computational domain is embedded within an extended, generally simply shaped domain that can be easily meshed, e.g. by a regular grid of square or cube-shaped elements. The original domain is retained by defining an indicator function α, which is 1 within its interior and attains a small value α0 in the fictitious part outside. Formally, this indicator function is multiplied to suitable material parameters in a weak formulation of the PDE to be solved. For a model problem in structural mechanics, α thus adds material of very low stiffness in the exterior part. This introduces a modeling error through the ‘fictitious stiffness’. Although this error is small and can be controlled by adjustment of α0, a p-extension of the FCM is asymptotically inconsistent. The situation is different in the case of an h-extension, regardless of the polynomial degree of the Ansatz space. We analyze this modeling error and show for a suitable h-extension an asymptotic convergence of h1/2, independent of the spatial dimension. The analysis is based on Strang’s second lemma and verified through numerical examples.