Permeable concrete is an environmentally friendly material that improves water permeability and slip resistance. The manuscript describes a new study aimed at improving the strength of permeable concrete obtained using local materials for the partial replacement of cement with rice and wheat straw ash due to the high amount of silica and pozzolanic characteristics present in the ash. For this purpose, nine concrete mixes were made (Phase I). The mixes were classified into four groups: Group A, with cement/aggregate ratios of 0.23, 0.34, and 0.44 for Mixes 1, 2, and 3, respectively; Group B, with sand added at 10% and 15% to the coarse aggregate for Mixes 4 and 5; Group C, with rice straw ash replacement ratios of 10% and 15% in the cement for Mixes 6 and 7; and, finally, Group D with wheat straw ash replacement ratios of 10% and 15% in the cement for Mixes 8 and 9. For Groups B to D, the water/binder ratio was 0.238. Fresh and hardened concrete tests were conducted. The results showed that Mixes C and D, which contained rice and wheat straw ash, increased the compaction factor due to their spherical shape and higher surface area compared with traditional pervious concrete. Additionally, permeability and porosity increased slightly for the mixes using rice and wheat straw ash. This could be attributed to increasing the interconnected voids. Optimum porosity was reached with 15% rice straw ash. The optimum mix design from Phase I was used in Phase II. Therefore, six pervious concrete slabs, reinforced with different types of reinforcement, were tested under flexural load. With the help of ANSYS, a finite element model was created to verify the results of experiments. The results of the numerical simulation are consistent with the results of the experiment. This article represents a definite step to new knowledge in the field of research of permeable concrete obtained using the partial replacement of cement with rice and wheat straw ash. Hence, this form of concrete can be used for parking lot paving, sludge beds for sewage plants, swimming pool surfaces, bridge walkways, zoo area floors, and animal barns. This concrete can also be used in applications requiring lightweight concrete.