We study the photoevaporation of molecular clumps exposed to a UV radiation field including hydrogen-ionizing photons (h nu > 13.6 eV) produced by massive stars or quasars. We follow the propagation and collision of shockwaves inside clumps and take into account self-shielding effects, determining the evolution of clump size and density with time. The structure of the ionization-photodissociation region is obtained for different initial clump masses (M = 0.01- 10(4)M(circle dot)) and impinging fluxes (G(0) = 10(2)-10(5) in units of the Habing flux). The cases of molecular clumps engulfed in the HII region of an OB star and clumps carried within quasar outflows are treated separately. We find that the clump undergoes in both cases an initial shock-contraction phase and a following expansion phase, which lets the radiation penetrate in until the clump is completely evaporated. Typical evaporation time-scales are similar or equal to 0.01 Myr in the stellar case and 0.1 Myr in the quasar case, where the clump mass is 0.1 M-circle dot and 10(3)M(circle dot) , respectively. We find that clump lifetimes in quasar outflows are compatible with their observed extension, suggesting that photoevaporation is the main mechanism regulating the size of molecular outflows.