Cylindrical SiOC foam filaments with a radial gradient in pore cell size were processed by continuous extrusion foaming of a methyl polysilsesquioxane. Upon leaving the extrusion nozzle foaming was initiated by pressure release which caused precipitation of supersaturated carbon dioxide from the polymer filament. Rapid cooling of the thin filaments generates a radial gradient of melt viscosity which gives rise for formation of closed cell morphology of isotropic pore cells in the core (diameter < 200 µm) and non-isotropic pore cells near the sur-face (shell; <20 µm). After pyrolysis at temperatures ranging from 800 to 1400 °C the stabilized polymer gradient foams were converted into closed cell SiOC ceramic gradient foams. XRD reveals the SiOC residue to be amorphous up to 1200 °C whereas crystallization of ß-SiC was observed at 1400 °C. A superior compressive strength of 9 MPa and a Young´s modulus of 7 GPa at a relative density of 0.18 were measured at an optimum pyrolysis temperature of 1000 °C.