NASA's Genesis Discovery Mission is designed to collect solar matter and return it to earth for analysis. The mission consists of launching a spacecraft that carries high purity collector materials, inserting the spacecraft into a halo orbit about the L1 sun-earth libration point, exposing the collectors to the solar wind for two years, and then returning the collectors to earth. The collectors will then be made available for analysis by various methods to determine the elemental and isotopic abundance of the solar wind. In preparation for this mission, potential collector materials are being characterized to determine baseline impurity levels and to assess detection limits for various analysis techniques. As part of the effort, potential solar wind collector materials have been analyzed using resonance ionization mass spectrometry (RIMS). RIMS is a particularly sensitivity variation of secondary neutral mass spectrometry that employs resonantly enhanced multiphoton ionization (REMPI) to selectively postionize an element of interest, and thus discriminates between low levels of that element and the bulk material. The high sensitivity and selectivity of RIMS allow detection of very low concentrations while consuming only small amounts of sample. Thus, RIMS is well suited for detection of many heavy elements in the solar wind, since metals heavier than Fe are expected to range in concentrations from 1 ppm to 0.2 ppt. In addition, RIMS will be able to determine concentration profiles as a function of depth for these implanted solar wind elements effectively separating them from terrestrial contaminants. RIMS analyses to determine Ti concentrations in Si and Ge samples have been measured. Results indicate that the detection limit for RIMS analysis of Ti is below 100 ppt for 106 averages. Background analyses of the mass spectra indicate that detection limits for heavier elements will be similar. Furthermore, detection limits near 1 ppt are possible with higher repetition rate lasers where it will be possible to increase signal averaging to 108 laser shots.