This paper analyzes laser and etching parameters to fabricate open and continuous microchannels and stacks of such microchannels in the bulk of crystalline sapphire (α-Al2O3). The structures are produced using a two-step method consisting of laser irradiation and selective etching. Infrared femtosecond laser pulses are focused in the bulk to locally render the crystalline material into amorphous. The amorphous material is, then, selectively etched in hydrofluoric acid. Amorphous sapphire shows a high etching selectivity in comparison to its crystalline state, which makes this material very attractive for a use with this technique. However, some of its properties make the processing challenging, especially during the laser-induced amorphization phase. This paper studies the effect of laser parameters by a step-by-step approach to fabricate long structures (longest dimensions up to millimeters) of different shapes inside the bulk of sapphire. The minimum cross-sectional dimensions of the resulting structures (microchannels) vary from few hundreds of nanometers for the smallest channels to tens of micrometers for the largest stacks of microchannels. The effect of the variation of repetition rate, pulse energy and channel-to-channel distance on the microchannels and stacks of microchannels is studied. SEM micrographs of polished cross-sections are used for performing a quantitative and qualitative analysis of the morphology of the structures after laser irradiation and, subsequently, after selective wet chemical etching.