  Despite the fact that existence of {\eta}-mesic nuclei in which the {\eta}
meson might be bound with the light nucleus by means of the strong interaction
was postulated already in 1986, it is still not experimentally confirmed.
Discovering of this new kind of an exotic nuclear matter is very important as
it might allow for better understanding of {\eta} meson structure and its
interaction with nucleons. The search of the {\eta}-helium bound states is
carried out at the COSY accelerator in the Research Center Juelich in Germany,
by means of the WASA detection system. The search are conducted with high
statistic and high acceptance for the free production of the 4He-{\eta} bound
states. It is also considered to search for {\eta}-tritium in quasi free
reaction which might be realised with COSY-TOF facility. In this thesis the
results of the Monte Carlo simulations of the {\eta}-helium bound states and
{\eta}-tritium bound state are presented and discussed. The acceptances of the
WASA-at-COSY and COSY-TOF detectors for the free and quasi-free {\eta}-mesic
nuclei production reactions were determined, respectively. Furthermore
acceptances were compared for three different models of nucleon momentum
distribution inside atomic nuclei and three different values of width of a
considered bound states. In case of COSY-TOF detector it was established that
the most effcient measurement of quasi-free dd --> p_sp (T-{\eta})_bs --> p_sp
dp{\pi}- reaction can be done at beam momentum of p_beam =3.1GeV/c.
