We propose two designs of effectively single mode porous polymer fibers for low-loss guiding of terahertz radiation. First, we present a fiber of several wavelengths in diameter containing an array of sub-wavelength holes separated by sub-wavelength material veins. Second, we detail a large diameter hollow core photonic bandgap Bragg fiber made of solid film layers suspended in air by a network of circular bridges. Numerical simulations of radiation, absorption and bending losses are presented; strategies for the experimental realization of both fibers are suggested. Emphasis is put on the optimization of the fiber geometries to increase the fraction of power guided in the air inside of the fiber, thereby alleviating the effects of material absorption and interaction with the environment. Total fiber loss of less than 10 dB/m, bending radii as tight as 3 cm, and fiber bandwidth of approximately 1 THz is predicted for the porous fibers with sub-wavelength holes. Performance of this fiber type is also compared to that of the equivalent sub-wavelength rod-in-the-air fiber with a conclusion that suggested porous fibers outperform considerably the rod-in-the-air fiber designs. For the porous Bragg fibers total loss of less than 5 dB/m, bending radii as tight as 12 cm, and fiber bandwidth of approximately 0.1 THz are predicted. oupling to the surface states of a multilayer reflector facilitated by the material bridges is determined as primary mechanism responsible for the reduction of the bandwidth of a porous Bragg fiber. In all the simulations, polymer fiber material is assumed to be Teflon with bulk absorption loss of 130 dB/m.