Abstract. By employing a refined version of the P´olya type integralinequality and other techniques, the authors establish some inequalitiesand absolute monotonicity for modified Bessel functions of the first kindwith nonnegative integer order. 1. Main resultsIt is well known that modified Bessel functions of the first kind I ±ν (z) aresolutions of the differential equationz 2 d 2 wdz 2 +zdwdz−z 2 +ν 2 w = 0.They are holomorphic functions of z throughout the z-plane cut along thenegative real axis, and are entire functions of ν for fixed z 6= 0. When ν = ±n,I ν (z) are entire functions of z. In [1, p. 375, 9.6.7], it is listed thatI ν (z) =X ∞k=0 1k!Γ(ν +k +1)z2 2k+ν , z ∈ C, ν ∈ R\{−1,−2,...},whereΓ(z) = lim n→∞ n!n z Q nk=0 (z +k), z ∈ C\{0,−1,−2,...}is the classical gamma function, see [1, p. 255, 6.1.2].On [12, p. 63], the following three double inequalities are derived:1− z/21+ z/2 0, ν ≥ −12; Received July 18, 2015.2010 Mathematics Subject Classification. Primary 33C10; Secondary 26A48, 26D15,44A10.Key words and phrases. inequality, absolute monotonicity, complete monotonic function,modified Bessel function of the first kind, P´olya type integral inequality.