Formation of thick, high energy density, flexible solid supercapacitors is challenging because of difficulties infilling gel electrolytes into porous electrodes. Incomplete infilling results in a low capacitance and poor mechanical properties. Here we report a bottom-up infilling method to overcome these challenges. Electrodes up to 500 μm thick, formed from multi-walled carbon nanotubes and a composite of poly(3,4-ethylenedioxythiophene), polystyrene sulfonate and multi-walled carbon nanotubes are successfully infilled with a polyvinyl alcohol/phosphoric acid gel electrolyte. The exceptional mechanical properties of the multi-walled carbon nanotube-based electrode enable it to be rolled into a radius of curvature as small as 0.5 mm without cracking and retain 95% of its initial capacitance after 5000 bending cycles. The areal capacitance of our 500 μm thick poly(3,4-ethylenedioxythiophene), polystyrene sulfonate, multi-walled carbon nanotube-based flexible solid supercapacitor is 2662 mF cm-2 at 2 mV s-1, at least five times greater than current flexible supercapacitors.