A four-level, plane wave model is proposed for a resonantly pumped $1.6\mu \mathrm{m}$ ${\mathrm{Er}}^{3+}$ laser, including the effect of upconversion. A mean population approximation leads to analytical expressions for the threshold and slope efficiency that are highly accurate compared to the numerical solution. Using the beam area as an adjustable parameter, the threshold and slope efficiency agree well with data obtained using a 1% Er:YAG crystal, pumped at $1470\mathrm{nm}$ , lasing at $1617\mathrm{nm}$ , in the range $0–100°\mathrm{C}$ . According to the model for this laser, the slope efficiency versus absorbed pump power is unaffected by upconversion, but the threshold is increased by a factor of 2–3. The results are important for choosing the optimum doping level and fiber or rod length.