We discuss the spectral energy distributions of FU Orionis variables, using new ground-based infrared photometry and IRAS ADDSCAN measurements. Nearly half of the recognized FU Orionis variables are heavily extincted, so further analysis is difficult. Three (V1057 Cyg, V1515 Cyg, Z CMa) of the remaining five objects have much larger far-infrared fluxes than can be explained by the simple accretion disk models that match their spectral energy distributions for lambda < 10-mu-m. The 10-20-mu-m excess emission in V1057 Cyg has decreased proportionately with the decline in optical light, which demonstrates that the far-infrared flux arises in a dust shell reprocessing light from the central object. The amount of dust required to explain the far-infrared excess emission of V1057 Cyg is much larger than that implied by the optical extinction, so the dust distribution is not spherically symmetric. In principle, a geometrically flared disk can account for the far-infrared emission, but in practice the large solid angle the disk must subtend at the star appears difficult to achieve in a resonable physical model. We suggest instead that the far-infrared excesses arise in somewhat flattened dusty envelopes with a covering factor in solid angle of roughly 1/2, which is consistent with the fraction of FU Orionis variables that are heavily embedded. The dusty envelope in V1057 Cyg must have an inner radius of approximately 10 AU to explain the excess emission at 10-mu-m, and this envelope probably cannot be static so close to the central star. We propose that the dusty envelope falls onto the outer disk at a rate of approximately 5 x 10(-6) M. yr-1. This rate is sufficient to replenish disk material accreted during a FU Orionis outburst and allow repetitive eruptions on time scales of several thousand years.