The kinetics and thermodynamics of loop formation by short segments of double-stranded DNA was studied by computer simulation. The DNA molecule was modeled as a discrete wormlike chain. Brownian dynamics was used to simulate the dynamic properties of the chain. Since the average time of loop formation, tau(a), grows sharply when the loop size drops below DNA persistence length, we were unable to simulate the process directly for such small loops. Instead, we used the relationship between the equilibrium probability of loop formation, P, tau(a), and the average time of loop decay, tau(d). The values of P and za were simulated directly. A new Monte Carlo algorithm was developed allowing efficient calculation of P for small DNA loops. The algorithm is also applicable to more complex models of a polymer chain, particularly to DNA models with intrinsic curvature. We also considered loop formation by a segment of a DNA molecule and found that the values of tau(d) and tau(a), are weakly affected by the total chain size. Our results showed that the formation of small loops is a very slow process: for loops less than 50 nn in size tau(a) can be comparable to the lifetime of the cell.