Summary: We investigate the properties of the multi-poly-Cauchy numbers \(c_n^{(k_1,\dots,k_r)}\) and polynomials \(c_n^{(k_1,\dots,k_r)}(z)\), which are generalizations of poly-Cauchy numbers \(c_n^{(k)}\) and polynomials \(c_n^{(k)}(z)\), introduced by the third author. We also study a complex variable function \(Z_{(k_1,\dots,k_r)}(s, z)\) interpolating the multi-poly-Cauchy polynomial \(c_n^{(k_1,\dots,k_r)}(z)\).