The aim of this work was to understand possible fast neutron contribution to background signals in the Semiconductor Tracker (SCT) of the ATLAS detector which is built on LHC at CERN. We measured current pulses induced by fast-neutron reactions in silicon pad detectors. Neutrons were produced at the Rez cyclotron by means of the (p,n) reaction on a thick beryllium target. Current pulses were stored by a fast digital oscilloscope for off-line analysis. Pulse-height spectra, corresponding to neutron interactions in the detector mainly due to (n,p) and (n,alpha) reactions, were obtained by integration of the pulses. The sensitivity of the detector against neutrons was estimated from analysis of the distribution of time intervals between two subsequent pulses. The neutron-induced signals correspond to an average energy deposition of several MeV and arise in the silicon detector of 1 cm^2 area with an average time spacing of about 575 micros. Results are compared with Monte-Carlo simulations.