Motivated by fundamental optimization problems in video delivery over wireless networks, we consider the
following problem of {\em packing resizable items (PRI)}.
Given is a bin of capacity $B > 0$, and a set $I$ of items. Each item $j \in I$ is of size $s_j >0$.
A packed item must stay in the bin for a fixed time interval. To accommodate more items in the bin,
each item $j$ can be {\em compressed} to a size $p_j \in [0,s_j)$ for at most a fraction
$q_j \in [0,1)$ of the packing interval. The goal is to pack in the bin, for the given time interval,
a subset of items of maximum cardinality.
PRI is strongly NP-hard already for highly restricted instances.
Our main result is an approximation algorithm that packs, for any instance $I$ of PRI, at least $\frac{2}{3}OPT(I) -3$
items, where $OPT(I)$ is the number of items packed in an optimal solution.
Our algorithm yields better ratio for instances in which the maximum compression time
of an item is $q_{max} \in (0, \frac 1 2)$. For subclasses of instances arising in
realistic scenarios, we give an algorithm that packs at least $OPT(I)-2$ items. Finally, we show that a non-trivial
subclass of instances admits an {\em asymptotic fully polynomial time approximation scheme (AFPTAS)}.