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The application of a polymer brush in sensing, actuation, self-folding, among others acutely depends on the tuneable bending of a brush-grafted substrate caused by the stress in the brush. However, the stress in a stimuli-responsive brush has not been investigated. In this work, we study the stress in the stimuli-responsive planar polymer brushes of neutral water-soluble polymers with low to very high graft densities using strong stretching theory (SST). First, SST with the Langevin force-extension relation for a polymer chain is extended to the study of stimuli-responsive brushes. Stress profile and other properties of a Poly(N-isopropylacrylamide) (PNIPAm) brush are then obtained using the extended SST and an empirical Flory-Huggins parameter. The model predicts that the stress in a PNIPAm brush is inhomogeneous and compressive at all temperatures and graft densities. The resultant stress is predicted to increase in magnitude with increasing graft density. Moreover, it decreases in magnitude with an increase in temperature before plateauing in low graft density brushes. In contrast, its magnitude increases weakly with increasing temperature in high density brushes. This contrasting behavior is traced to the minimum in interaction free energy density \emph{vs} polymer volume fraction curve for PNIPAm solution at a large volume fraction, and stiffening of chains due to finite extensibility. Furthermore, our results indicate that the ability to tune the resultant stress by changing temperature diminishes with increasing graft density.