A Monte Carlo code to solve the transfer of Lyα photons is developed that can predict the Lyα image and two-dimensional Lyα spectra of a hydrogen cloud with any given geometry, Lyα emissivity, neutral hydrogen density distribution, and bulk velocity field. We apply the code to several simple cases of a uniform cloud to show how the Lyα image and emitted line spectrum are affected by the column density, internal velocity gradients, and emissivity distribution. We then apply the code to two models for damped Lyα absorption systems: a spherical, static, isothermal cloud and a flattened, axially symmetric, rotating cloud. If the emission is due to fluorescence of the external background radiation, the Lyα image should have a core corresponding to the region where hydrogen is self-shielded. The emission-line profile has the characteristic double peak with a deep central trough. We show how rotation of the cloud causes the two peaks to shift in wavelength as the slit is perpendicular to the rotation axis and how the relative amplitude of the two peaks is changed. In reality, damped Lyα systems are likely to have a clumpy gas distribution with turbulent velocity fields, which should smooth the line emission profile but should still leave the rotation signature of the wavelength shift across the system.
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