Reliability　analysis　of　dynamic　structural　systems　and　its　implications　for　structural　design　have　garnered　increasing　attention.　Sample-based　methods　prove　insensitive　to　the　dimension　of　the　probability　integral.　Nontheless,　a　substantial　number　of　realizations　is　necessary　for　estimating　small　failure　probabilities,　resulting　in　time-consuming　computations.　Recently,　the　Directional　Importance　Sampling　(DIS)　was　introduced　for　linear　structural　systems　subjected　to　Gaussian　loads,　showcasing　the　ability　to　accurately　estimate　small　failure　probabilities　with　a　reduced　number　of　simulations.　However,　this　Gaussian　assumption　on　the　load　makes　the　method　inapplicable　for　realistic　loading　scenarios　as　they　might　be　of　non-Gaussian　nature.　This　contribution　develops　the　DIS　method　for　linear　structural　systems　subjected　to　loading　characterized　as　non-Gaussian　white　noise.　To　take　the　advantage　of　both　linearity　in　physical　space　and　simplicity　of　Gaussian　space,　directional　importance　sampling　is　conducted　in　Gaussian　space　and　the　failure　probability　is　estimated　with　the　aid　of　physical　space.　The　information　is　dynamically　exchanged　between　physical　and　Gaussian　spaces　with　the　aid　of　normal　and　inverse-normal　transformation　techniques.　The　whole　procedure　of　the　developed　DIS　method　is　straightforward,　and　it　provides　an　explicit　estimator　of　the　failure　probability.　The　application　of　the　developed　DIS　method　is　presented　through　three　examples,　illustrating　its　accuracy　and　efficiency　for　dynamic　reliability　analysis.　©　2024　The　Author(s)