Summary: The author discuses the system failure probability of the model 2-within-consecutive (2, 2) out of (n, m) system for special values of \(m\). The basic idea for evaluating the failure probability was the usage of the number of configurations of \(k\) \((k = 2, 3, 4)\) parallel columns each containing \(n\) components in a \(2\times 2\)-matrix. The equation for the linear \(k\)-within \((r, s)\) out of \((n, m)\) system is obtained. In this study the failure probability of 2-within-consecutive (2, 2) out of \((n, m)\) system for \(m = 2, 3, 4\) is given. In general, it was difficult to evaluate the failure probability in two-dimensional reliability structures such as the linear \(k\)-within \((r, s)\) out of \((n, m)\) system. The researcher established the failure probability and then the reliability of three special cases. It is recommended to generalize the results for any values of \(k\), \(r\), \(s\) and \(m\).