Canonical molecular dynamics simulations are performed to investigate the behavior of single-chain and multiple-chain poly(ethylene glycol) (PEG) contained within a cubic framework spanned by polyethylene (PE) chains. This simple model is the first of its kind to study the chemical physics of polymer-threaded organic frameworks, which are materials with potential applications in catalysis and separation processes. For a single-chain 9-mer, 14-mer, and 18-mer in a small framework, the PEG will interact strongly with the framework and assume a more linear geometry chain with an increased radius of gyration Rg compared to that of a large framework. The interaction between PEG and the framework decreases with increasing mesh size in both vacuum and water. In the limit of a framework with an infinitely large cavity (infinitely long linkers), PEG behavior approaches simulation results without a framework. The solvation of PEG is simulated by adding explicit TIP3P water molecules to a 6-chain PEG 14-mer aggregate confined in a framework. The 14-mer chains are readily solvated and leach out of a large 2.6 nm mesh framework. There are fewer water PEG interactions in a small 1.0 nm mesh framework, as indicated by a smaller number of hydrogen bonds. The PEG aggregate, however, still partially dissolves but is retained within the 1.0 nm framework. The preliminary results illustrate the effectiveness of the simple model in studying polymer-threaded framework materials and in optimizing polymer or framework parameters for high performance.