  The effects of magnetic fields on Big Bang Nucleosynthesis(BBN) have been
calculated, and the impact on the abundances of the light elements have been
investigated numerically. An upper limit on the strength of primordial magnetic
fields compatible with observations of light element abundances has been thus
obtained. In the framework of standard BBN theory, the maximum strength of the
primordial magnetic fields, on scales greater than $10^4$cm but smaller than
the event horizon at the BBN epoch ($\sim 1$ min., $\sim 2\times 10^{12}$cm),
is $\le 10^{11}$ Gauss. This limit is shown to allow magnetic fields at the
time of recombination no stronger than $\sim 0.1$ gauss on scales $\ge
10^{11}{\rm cm}$. Our results also strongly indicate that, at the BBN epoch,
and for field strengths $B\le10^{13}$gauss, the effects of magnetic fields on
the primordial abundances of light elements are dominated by effects from
reaction rates in the presense of primeval magnetic fields rather than by
magnetic density effects on the expansion rate.
