The lattice parameters of stoichiometric $UO_2$ and $U_{1-y}Er_{y}O_2$ in the range of y=0.01 to y =0.33 were determined with use of X-ray diffraction data. Oxygen potentials have been measured by means of a thermogravimetric method in the range of 1200~$1500^{circ}C$ and $10^{-14}$ $leq$ $Po_2$ $leq$ $10^{-3}$ for pure $UO_2$ and $U_{1-y}Er_{y}O_{2{pm}x}$ solid solutions with y=0.02, y=0.06 and y=0.20, respectively. Their oxygen partial pressures were maintained by controlling $CO_2$/CO mixture atmosphere, and the $Po_2$ values corresponding to x of $U_{1-y}Er_{y}O_{2{pm}x}$ solid solutions were measured with an electrolyte oxygen sensor. The lattice parameter decreases linearly with an increase in the erbium content. The change of the lattice parameter can be expressed in a linear equation of y as a($AA$) =5.4695-0.220y for 0 $leq$y$leq$0.33. The experimental coefficient of y -0.220 in $U_{1-y}Er_{y}O_2$ was an intermediate value between the calculated values -0.273 and -0.156 in the case of $U^{5+}$ and $U^{6+}$, respectively. The (equation omitted) has been found to undergo abrupt increase in the range of -360 to -270 kJ/mole for y=0.06 and -320 to -220 H/mole for y=0.20, respectively, in the temperature range of 1200-$1500^{circ}C$. (equation omitted) increases with erbium content, but the effect of the dopant for x =0.01 is less significant than that for stoichiometry. The oxygen potentials for $UO_2$ and $U_{0.98}Er_{0.02}O_{2+x}$ can be approximately represented by the $U^{5+}$/$U^{4+}$ model but those for y$geq$ 0.06 in $U_{1-y}Er_{y}O_{2{pm}x}$ solid solutions cannot be interpreted by the mean uranium valence model.