Interpolation search is an efficient algorithm for searching ordered tables. When the entries are order statistics from a uniform distribution, interpolation search takes an average of lg lg n + O(1) accesses to locate a given value in the table, where n is the table size. By locate, we mean the following: if the value is in the table, its position in the table is found, or, if the value is not in the table, then two consecutive values straddling it are found. While interpolation search has been extensively analyzed, it has not been extensively simulated to determine, empirically, the distribution of the number of accesses required to locate a random value in a random table. A few simulation studies have been conducted for small values of n, by generating a sample of independent uniform random variables, sorting them, and performing the search. This is very expensive because sorting takes up a lot of time, especially for large tables. We use simple results in mathematical statistics to design an efficient algorithm for simulating an interpolation search that uses no more than the exact number of table entries that are actually compared with the searched value during any search. We also present our simulation results.