We use the toy model of baryon bag formation to study the changes in the structure of a nucleon when it is placed in nuclear matter. Several interesting qualitative results have been found. We find that ${\mathit{M}}^{\mathrm{*}}$, the nucleon mass in nuclear matter, does not scale with ${\mathit{F}}_{\mathrm{\ensuremath{\pi}}}^{\mathrm{*}}$, the latter being the value of the \ensuremath{\sigma} field in nuclear matter. The product ${\mathit{M}}^{\mathrm{*}}$〈${\mathit{r}}^{2}$${\mathrm{〉}}^{1/2\mathrm{*}}$ is nearly independent of nuclear density. The coupling constant ${\mathit{g}}_{\mathrm{\ensuremath{\sigma}}\mathit{N}\mathit{N}}^{\mathrm{*}}$ decreases with density. The coupling constant ${\mathit{g}}_{\mathrm{\ensuremath{\pi}}\mathit{N}\mathit{N}}^{\mathrm{*}}$/2${\mathit{M}}^{\mathrm{*}}$ and the rho-nucleon tensor coupling constant, ${\mathit{f}}_{\mathrm{\ensuremath{\rho}}\mathit{N}\mathit{N}}^{\mathrm{*}}$/2${\mathit{M}}^{\mathrm{*}}$, increase with density at the same rate. The coupling constants ${\mathit{g}}_{\mathrm{\ensuremath{\omega}}\mathit{N}\mathit{N}}^{\mathrm{*}}$ and ${\mathit{g}}_{\mathrm{\ensuremath{\rho}}}^{\mathrm{*}}$ also increase at the same rate, but the rate itself is low. We find that ${\mathit{M}}^{\mathrm{*}}$+${\mathit{g}}_{\mathrm{\ensuremath{\sigma}}\mathit{N}\mathit{N}}^{\mathrm{*}}$(${\mathit{F}}_{\mathrm{\ensuremath{\pi}}}$-${\mathit{F}}_{\mathrm{\ensuremath{\pi}}}^{\mathrm{*}}$) is approximately independent of the nuclear density. The magnetic moments increase, while ${\mathit{g}}_{\mathit{A}}^{\mathrm{*}}$(0) decreases. At half the normal density these changes are in the range 3--7 % depending on the parameters used. We discuss briefly the implications of these results on the properties of nuclear matter.