We characterize laser-induced damage threshold (LIDT) in transparent photopolymers by a sub-ps laser pulses of 515 nm wavelength representing case of high light intensities. Five different photopolymers (SZ2080, OrmoComp, SU-8, PDMS and PMMA) widely used in the laser lithography are investigated. The relationship of the damage threshold and optical band-gap energy of the polymers indicating possible damage mechanism is considered. Incubation model validating damage threshold dependence on the number of laser pulses is studied as well. The obtained characteristic values of LIDT reveal potential of photopolymers and their possible applications in high power laser systems.