A model is presented that seeks to explain quantitatively the stellar abund
ances of r-process elements and other elements associated with the r-proces
s sites. It is argued that the abundances of all these elements in stars wi
th -3 less than or similar to [Fe/H] < -1 can be explained by the contribut
ions of three sources. The sources are the first generations of very massiv
e (<greater than or similar to> 100 M.) stars that are formed from big bang
debris and are distinct from Type II supernovae (SNe II) and two types of
SNe II, the H and L events, which can occur only at [Fe/H] greater than or
similar to -3. The H events are of high frequency and produce dominantly he
avy (A > 130) r-elements but no Fe (presumably leaving behind black holes).
The L events are of low frequency and produce Fe and dominantly light (A l
ess than or similar to 130) r-elements (essentially none above Ba). By usin
g the observed abundances in two ultra-metal-poor stars and the solar r-abu
ndances, the initial or prompt inventory of elements produced by the first
generations of very massive stars and the yields of H and L events can be d
etermined. The abundances of a large number of elements in a star can then
be calculated from the model by using only the observed Eu and Fe abundance
s. To match the model results and the observational data for stars with -3
< [Fe/H] < -1 requires that the solar r-abundances for Sr, Y, Zr, and Ba mu
st be significantly increased from the standard values. No such changes app
ear to be required for all other elements. If the changes in the solar r-ab
undances for Sr, Y, Zr, and Ba are not permitted, the model fails at -3 < [
Fe/H] < -1 but still works at [Fe/H] approximate to -3 for these four eleme
nts. By using the corrected solar r-abundances for these elements, good agr
eement is obtained between the model results and data over the range -3 < [
Fe/H] < -1. No evidence of s-process contributions is found in this region,
but all the observational data in this region now show regular increases o
f Ba/Eu above the standard solar r-process value. Whether the solar r-compo
nents of Sr, Y, Zr, and Ba used here to obtain a Dt to the stellar data can
be reconciled with those obtained from solar abundances by subtracting the
s-components calculated from models is not clear.