Two variations of two-dimensional problem of packing square objects are considered: strip packing and bin packing. The strip packing problem is to pack the squares into a strip of width 1 so as to minimize the span of the packing. The bin-packing problem is to pack squares into square bins of size 1 so as to minimize the number of bins. Efficient approximation algorithms for both problems are devised and their probabilistic performance analysis is presented for the case in which the square sizes are drawn independently from the uniform distributionon [0,1]. In a probabilistic sense, these algorithms give packings closer to optimal than algorithms previously considered for rectangle packing.