Fitting spectral distributions of total fluxes or image intensities are two standard methods for estimating the masses of starless cores and protostellar envelopes. The major source and basis of our knowledge of the origin and evolution of self-gravitating cores and protostars, such mass estimates are uncertain. In this model-based study, a grid of radiative transfer models of starless cores and protostellar envelopes was computed and their total fluxes and image intensities were fitted to derive the model masses. To investigate intrinsic effects related to the physical objects, all observational complications were explicitly ignored. Known true values of the numerical models allow us to assess the qualities of the methods and fitting models, as well as the effects of nonuniform temperatures, far-infrared opacity slope, selected subsets of wavelengths, background subtraction, and angular resolutions. The method of fitting image intensities gives more accurate masses for more resolved objects than the method of fitting total fluxes. With the latter, a fitting model that assumes optically thin emission gives much better results than the one allowing substantial optical depths. Temperature excesses within the objects above the mass-averaged values skew their spectral shapes towards shorter wavelengths, leading to masses underestimated typically by factors 2-5. With a fixed opacity slope deviating from the true value by a factor of 1.2, derived masses are inaccurate within a factor of 2. The most accurate masses of the models are estimated by fitting just two or three longest-wavelength fluxes. Conventional algorithm of background subtraction is a likely source of large systematic errors. The absolute values of masses of the unresolved or poorly resolved objects in star-forming regions are uncertain to within at least a factor of 2-3.
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