The objective of the present study is to investigate the safety parameters and their safety margins for a typical MTR pool type research reactor during a partial loss of flow or core bypass without scram. The proposed reactor is a plate type fuel element with upward core flow. The code used in the analysis is RELAP5/MOD3.3, the well-known thermal hydraulic system code. Different causes for the partial loss of flow may occur such as, circulation pump degradation, one of the flapper valves fail to tightly close, small break in the cold leg, etc. In the proposed postulated accident, an exponential decrease of the core flow rate is assumed to occur with a time constant of 25 s to 20, 40, 60, and 80% of the nominal core flow, as the new steady state values. Study results for thermal hydraulic reactor behavior were validated by comparing RELAP5 results with published results of PARET code under the same accident conditions. Also, the safety parameters and margins were calculated. From comparisons, good agreements are found between RELAP5 code results and PARET code results for the maximum coolant, clad, and fuel temperatures, as well as minimum DNBR values. Deviations are found between the results of the two codes for flow instability parameter. But, both of the two codes concluded that fuel integrity criteria, in terms of thermal hydraulic instability, are not exceeded. In the second part of the study, the effect of decreasing the time constant on the transient results was studied.