Context : PAHs appear to be an ubiquitous interstellar dust component but the effects of shocks waves upon them have never been fully investigated . Aims : We study the effects of energetic ( \approx 0.01 - 1 keV ) ion ( H , He and C ) and electron collisions on PAHs in interstellar shock waves . Methods : We calculate the ion-PAH and electron-PAH nuclear and electronic interactions , above the threshold for carbon atom loss from a PAH , in 50 - 200 km s ^ { -1 } shock waves in the warm intercloud medium . Results : Interstellar PAHs ( N _ { C } = 50 ) do not survive in shocks with velocities greater than 100 km s ^ { -1 } and larger PAHs ( N _ { C } = 200 ) are destroyed for shocks with velocities \geq 125 km s ^ { -1 } . For shocks in the \approx 75 - 100 km s ^ { -1 } range , where destruction is not complete , the PAH structure is likely to be severely denatured by the loss of an important fraction ( 20 - 40 % ) of the carbon atoms . We derive typical PAH lifetimes of the order of a few \times 10 ^ { 8 } yr for the Galaxy . These results are robust and independent of the uncertainties in some key parameters that have yet to be well-determined experimentally . Conclusions : The observation of PAH emission in shock regions implies that that emission either arises outside the shocked region or that those regions entrain denser clumps that , unless they are completely ablated and eroded in the shocked gas , allow dust and PAHs to survive in extreme environments .