A study was made of simplified procedures for estimating the fundamental period, T, of a linear or equivalent linear model of a soil profile. Closed form solutions and approximate methods for computing the first period of an elastic shear-beam representation of the profile were examined. Closed form solutions are presented in chart form for the following cases: (a) shear-wave velocity increasing as a power of depth, (b) shear modulus increasing or decreasing linearly with depth, (c) two-layer profile, and (d) overconsolidated or uniform crust on layer with modulus increasing with depth. Seven approximate methods developed to estimate the period of a layered soil profile without a computer were also discussed and evaluated. For this evaluation, the periods of 76 representative soil profiles were estimated by each one of the approximate methods, and the results compared with the exact values. Methods 6 (Successive Use of Two-Layer Solution) and 7 (Simplified Version of the Rayleigh Procedure) gave errors less than 10 per cent for the period in all cases considered, and these methods are recommended for practical use. The approximate methods and the closed form solution charts may be used to estimate the characteristic site period, Ts, included in the proposed (1976) modifications to the seismic provisions of the Unified Building Code.