To meet the growing requirements of Standard Positioning Services (SPS) and Precision Services (PS), more and more GNSS systems operating at conventional GPS frequencies and higher frequency bands are launched. The Indian NavIC system is one of such systems transmitting navigational signals at S1 (2492.028 MHz) and L5 (1176.45 MHz) frequencies. For GPS at L-band frequencies, comprehensive research work has been conducted to analyze the ionospheric delay to estimate precise user position, although very little research work is available in the public domain at the navigational S-band level. The NavIC program provides opportunities to explore the ionospheric delay effect on S-band navigational signals. The precise position determination demands accurate estimation of the vertical ionospheric delay which is generally obtained using Vertical Electron Content (VTEC) of the ionosphere. The VTEC can be obtained by multiplying a mapping function to the Slant Total Electron Content (STEC). Conventionally a thin shell (also known as a single shell) model is used to map STEC to VTEC, but it introduces error at low elevation angles. This error is significant for the NavIC receivers, located in the northern part of India, as they observe elevation angles below 50 • for most of the time, and thus there is a need to investigate the suitability of the mapping function model for the NavIC system. As the ionospheric shell height modifies the mapping function and results in a change in VTEC, the height and thickness of the thick shell have been investigated based on the ionospheric data taken from IRI 2016 and were estimated as 300 km and 250 km, respectively. In the present work, the thick shell model has been compared to thin shell model mapping functions to improve the accuracy of VTEC estimation at the low elevation. The reduction in vertical delay using the thick shell mapping function at low elevation indicates its suitability for the locations like Dehradun, India, which lies in the mid-latitude region. Furthermore, the temporal variability of vertical delay at S and L band frequencies has also been investigated to understand the diurnal and seasonal characteristics of ionospheric vertical delay over a period of 12 months to cover all the seasons during the year 2017-18. The vertical delay at the S-band frequency was found to be less than that at the L-band frequency and is almost constant over a month. This finding will be beneficial for single-frequency users and could be used to develop the Grid Ionospheric Vertical Delay (GIVD) map for the NavIC system to enhance positional accuracy.