Motivated by recent experiments showing the buckling of microtubules in cells, we study theoretically the mechanical response of, and force propagation along elastic filaments embedded in a non-linear elastic medium. We find that, although embedded microtubules still buckle when their compressive load exceeds the critical value $f_c$ found earlier, the resulting deformation is restricted to a penetration depth that depends on both the non-linear material properties of the surrounding cytoskeleton, as well as the direct coupling of the microtubule to the cytoskeleton. The deformation amplitude depends on the applied load $f$ as $(f- f_c)^{1/2}$. This work shows how the range of compressive force transmission by microtubules can be as large as tens of microns and is governed by the mechanical coupling to the surrounding cytoskeleton.
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