Spatially fractionated radiotherapy, also known as grid therapy (GRID), has been used for more than a century to try to treat several kinds of lesions. Yet, the grid technique remains a relatively unknown and uncommon treatment modality nowadays. Spatially fractionated beams, instead of conventional homogeneous fields, have been used to exploit the experimental finding that normal tissue can tolerate higher doses when smaller tissue volumes are irradiated. This increase in tolerance with reducing beam size is known as the dose-volume effect. Despite the fact that targets were given inhomogeneous dose distribution, sometimes with some volumes receiving close to no dose, good results in the form of shrinking of bulky tumors have been observed in palliative treatments. The biological processes responsible for this effect are still under discussion, with several possible causes. However, numerous experiments on mice, rats and pigs have confirmed the existence of such effect, which in turn motivates the present development of grid therapy.While mainly photons have been used in grid therapy, proton and ion grid therapies are also emerging as potential alternatives. In this work, an innovative form of grid therapy was proposed. Grids of proton beamlets were interlaced over a target volume with the intention of achieving two main objectives: (1) to keep the grid pattern (made of adjacent high and low doses) from the skin up to the vicinity of the target while (2) delivering nearly homogeneous dose to the target volume. This interlaced proton grid therapy was explored with the use of different beam sizes, from conventional sizes deliverable at modern proton facilities, down to millimeter sized beams. Other considerations that would prevent its clinical use, such as the variable relative biological effectiveness of protons or the use of cone beam computed tomography, were also evaluated. The overall aim was to assess if, and how, such treatment modality could be applied clinically, from a physics and dosimetry point of view. While it presented several theoretical advantages, its potential issues of concern and limitations were also evaluated.