We report on theoretical and experimental investigation of azimuthal and longitudinal modes in rolled-up microtubes at telecom wavelengths. These microtubes are fabricated by selectively releasing a coherently strained InGaAs/GaAs bilayer. We apply planar waveguide method and a quasi-potential model to analyze the azimuthal and longitudinal modes in the microtubes near 1550 nm. Then we demonstrate these modes in transmission spectrum by evanescent light coupling. The experimental observations agree well with the calculated results. Surface-scattering-induced mode splitting is also observed in both transmission and reflection spectra at ~1600 nm. The mode splitting is in essence the non-degeneracy of clockwise and counter-clockwise whispering-gallery modes of the microtubes. This study is significant for understanding the physics of modes in microtubes and other microcavities with three-dimensional optical confinement, as well as for potential applications such as microtube-based photonic integrated devices and sensing purposes.