Because white dwarfs are the most common end state of stellar evolution, determining their internal structure will yield many clues about the final stages of stellar evolution and the physics of matter under extreme conditions. We present the results of our parametric survey of evolutionary models of compositionally stratified white dwarfs with hydrogen surface layers (DA white dwarfs) and provide a comprehensive set of theoretical {ital g}-mode pulsation periods for comparison to observations of pulsating DA white dwarfs. This survey complements the previous survey of helium atmosphere (DB) white dwarf periods of Bradley, Winget, & Wood. We show how to use the periods of low-overtone and/or trapped modes to constrain the internal structure of pulsating DA white dwarfs by utilizing their sensitivity to the total stellar mass and the location of the hydrogen/helium transition zone. We use G117-B15A as an example to demonstrate the potential of our models for asteroseismology; we suggest that G117-B15A has a mass of 0.55 {ital M}{sub {circle_dot}} and a hydrogen layer mass of {approx_equal}1.5{times}10{sup {minus}4} {ital M}{sub {asterisk}}. {copyright} {ital 1996 The American Astronomical Society.}