Late Neogene and younger deformation in Cook Inlet basin is caused by dextral transpression in the plate margin of south-central Alaska. Collision and subduction of the Yakutat microplate at the northeastern end of the Aleutian subduction zone is driving the accretionary complex of the Chugach and Kenai Mountains toward the Alaska Range on the opposite side of the basin. This deformation creates belts of fault-cored anticlines that are prolific traps of hydrocarbons and are also potential sources for damaging earthquakes. The faults dip steeply, extend into the Mesozoic basement beneath the Tertiary basin fill, and form conjugate flower structures at some localities. Comparing the geometry of the natural faults and folds with analog models created in a sandbox deformation apparatus suggests that some of the faults accommodate significant dextral as well as reverse-slip motion. We develop a tectonic model in which dextral shearing and horizontal shortening of the basin is driven by microplate collision with an additional component of thrust-type strain caused by plate subduction. This model predicts temporally fluctuating stress fields that are coupled to the recurrence intervals of large-magnitude subduction zone earthquakes. The maximum principal compressive stress is oriented east-southeast to east-northeast with nearly vertical least compressive stress when the basin's lithosphere is mostly decoupled from the underlying subduction megathrust. This stress tensor is compatible with principal stresses inferred from focal mechanisms of earthquakes that occur within the crust beneath Cook Inlet basin. Locking of the megathrust between great magnitude earthquakes may cause the maximum principal compressive stress to rotate toward the northwest. Moderate dipping faults that strike north to northeast may be optimally oriented for rupture in the ambient stress field, but steeply dipping faults within the cores of some anticlines are unfavorably oriented with respect to both modeled and observed stress fields, suggesting that elevated fluid pressure may be required to trigger fault rupture.