This paper is to describe principles of laser optoacoustic tomography for medical diagnostics. Two types of imaging modes are presented. The first is the tomography in transmission mode, which utilizes detection of stress transients transmitted from the laser-excited volume toward the depth through thick layers of tissue. The second is the tomography in reflection mode which utilizes detection of stress transients generated in superficial tissue layer and reflected back toward tissue surface. To distinguish the two modes, we have abbreviated them as (1) laser optoacoustic tomography in transmission mode, LOATT, and (2) time-resolved stress detection tomography of light absorption, TRSDTLA, in reflection mode where emphasis is made on high spatial resolution of images. The basis for laser optoacoustic tomography is the time-resolved detection of laser-induced transient stress waves, selectively generated in absorbing tissues of diagnostic interest.