Some response statistics of a linear oscillator under impulsive‐noise forcing are examined from analytical as well as empirical viewpoints. Specifically, calculation of the first‐order probability density and the crest (level crossing) statistics of the response of a narrow‐band single‐degree‐of‐freedom system under Poisson noise loading are considered. The inability to obtain numerical results from the Gram—Charlier (Type A) series is noted, despite the discovery of a convenient recursion relation between the moments and the semi‐invariants of a random process. Under the simultaneous assumptions of a low impulse rate and high systemQ, analytic expressions for the response first‐order probability density and the response crest statistics are established that are in good agreement with experiment. Finally, a quantitative measure of the degree of deviation of the system random response from a Gaussian process is presented and discussed.