  Cosmic string loops are non-linear density fluctuations which form in the
early universe and could play an important role in explaining many phenomena
which are in tension with the standard $\Lambda$CDM model. Hence, the details
of the accretion process onto cosmic string loops should be studied in detail.
Most previous works view loops as point masses and ignore the impact of a
finite loop size. In this work, we utilize the Zel'dovich approximation to
calculate the non-linear mass sourced by a static extended loop with a
time-averaged density profile derived from the trajectory of the loop
oscillation, and compare the result with what is obtained for a point-mass
source. We find that the finite size of a loop mainly affects the evolution of
turnaround shells during the early stages of accretion, converging to the point
mass result after a critical redshift, $z^{(II)/(III)}_{c}$. For
$z>z^{(II)/(III)}_{c}$, the total accreted mass surrounding a loop is
suppressed relative to the point mass case and has a growth rate proportional
to $(1+z)^{-3/2}$. As an immediate extension, we also qualitatively analyse the
accretion onto moving point masses and onto moving extended loops. In addition
to the reduction in the nonlinear mass, the loop finite size also changes the
shape of the turnaround surface at early stages of accretion.
