In this work, we employ the class I approach to obtain wormhole solutions in the framework of general relativity in two different ways. Firstly, we propose a suitable red-shift function in order to find its associated shape function. Afterwards, we solve the inverse problem, namely, we impose the well known Morris–Thorne shape function to obtain the corresponding red-shift. It is found that, on one hand, the first model satisfies all the general requirements of a traversable wormhole. On the other hand, although the second solution violates the null energy condition at the throat as expected, the solution is not asymptotically flat. The study is complemented by analyzing the hydrostatic balance of the system by means of the modified relativistic hydrostatic equilibrium equation.