We search \(t\)-matrix poles for \(\Lambda N-\Sigma N\) coupling interactions using two soft core models of the Nijmegen group which bind the hypertriton at the correct binding energy, and hard core models which are still influential in hypernuclear physics. To treat the hard core potentials, a useful method for calculating the off-shell \(t\)-matrix is proposed. We find poles close to the \(\Sigma N\) threshold in the second or third quadrant of the complex plane of the \(\Sigma N\) relative momentum. The relation between the poles and the shape of the \(\Lambda N\) elastic total cross section is discussed based on a so-called uniformization by which two-channel \(t\)-matrices become single-valued on a complex valuable. We also find poles near the \(\Lambda N\) threshold. These are correlated to the \(S\)-wave \(\Lambda N\) scattering lengths, the values of which have yet to be determined.