Transient spectral absorption events monitored now for years towards the star beta Pictoris have been interpreted as resulting from the transit across the line of sight of evaporating star-grazing kilometer-sized bodies (Falling Evaporating Bodies, or FEBs). Several Herbig Ae/Be stars of various ages have been observed to exhibit somehow similar absorption events that have been attributed to similar FEB events. We investigate here this question from a modeling point of view. Adapting the FEB simulation code we had developed earlier specifically for beta Pic, to the case of typical Herbig Ae/Be stars, we try to derive in which conditions FEB-like objects may generate detectable transient absorption events. We compare these conditions with those found in the case of beta Pic. A major difference with beta Pic is that Herbig Ae/Be stars have strong stellar winds (10-9-10-7 M_sun yr-1). Those winds appear to have a drastic interaction with the gaseous material escaped from the FEBs. With the presence of such stellar winds, the spectral signatures of FEBs are not detectable, unless their mass loss rate is huge. This translates into very large bodies (~100 km size), instead of ~15 km for beta Pic FEBs. This appears unrealistic in terms of amount of planetesimal mass needed in the disks surrounding these stars. We discuss then the validity of the FEB hypothesis for specific example stars. It turns out that for the younger (a few 106 yr old) Herbig Ae/Be stars like AB Aur, with well identified winds gtrsim 10-8 M_sun yr-1, the variable features sometimes observed are not likely to be due to FEBs, unless produced in wind free cavities. For older (gtrsim 107 yr old) stars Herbig Ae/Be like HD 100546, the FEB scenario could still explain the spectral events observed, but either the wind must to be weaker than ~m10-10 M_sun yr-1 (which cannot be excluded so far), or the FEBs approach the star in wind free cavities.