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We present the Simple Intensity Map Producer for Line Emission (SIMPLE), apublic code for quickly simulating mock line-intensity maps, and an analyticalframework for modeling intensity maps including observational effects. SIMPLEcan be applied to any spectral line sourced by galaxies. The SIMPLE code isbased on lognormal mock catalogs of galaxies including positions and velocitiesand assigns luminosities following the luminosity function. After applying aselection function to distinguish between detected and undetected galaxies, thecode generates an intensity map, which can be modified with anisotropicsmoothing, noise, a mask, and sky subtraction, and calculates the powerspectrum multipoles. We show that the intensity autopower spectrum and thegalaxy-intensity cross-power spectrum agree well with the analytical estimatesin real space. We derive and show that the sky subtraction suppresses theintensity autopower spectrum and the cross-power spectrum on scales larger thanthe size of an individual observation. As an example application, we makeforecasts for the sensitivity of an intensity mapping experiment similar to theHobby-Eberly Telescope Dark Energy Experiment (HETDEX) to the cross-powerspectrum of Ly$\alpha$-emitting galaxies and the Ly$\alpha$ intensity. Wepredict that HETDEX will measure the galaxy-intensity cross-power spectrum witha high signal-to-noise ratio on scales of $0.04\, h\,\mathrm{Mpc}^{-1} < k <1\, h\,\mathrm{Mpc}^{-1}$.

SIMPLE: Simple Intensity Map Producer for Line Emission