Structural econometric models are used to combine economic theory and data to estimate parameters and counterfactuals, e.g. the effect of a policy change. These models typically make functional form assumptions, e.g. the distribution of latent variables. I propose a framework to characterize the sensitivity of structural estimands with respect to misspecification of distributional assumptions of the model. Specifically, I characterize the lower and upper bounds on the estimand as the assumption is perturbed infinitesimally on the tangent space and locally in a neighborhood of the model's assumption. I compute bounds by finding the gradient of the estimand, and integrate these iteratively to construct the gradient flow curve through neighborhoods of the model's assumption. My framework covers models with general smooth dependence on the distributional assumption, allows sensitivity perturbations over neighborhoods described by a general metric, and is computationally tractable, in particular, it is not required to resolve the model under any alternative distributional assumption. I illustrate the framework with an application to the Rust (1987) model of optimal replacement of bus engines.