Differential equations of motion of many systems moving in a fluid are described more accurately using a fractional derivative model. For example, a large plate completely immersed in a fluid medium and connected to a spring is defined by a second order differential equation containing a 3/2 order derivative term (Torvik and Bagley, 1984). A spherical particle moving in a viscous fluid experiences Basset force, which is described by a fractional derivative term (Basset, 1888; Mainardi, 1997; Tatom, 1988). It is therefore conjectured that a string moving in a fluid would experience a fractional damping force. Thus, many engineering applications containing strings and ropes such as open air high voltage transmission lines, bridges, and structures may require fractional derivatives to model them accurately.In this paper, we present a deterministic and stochastic model of a fractionally damped string. In this model, the viscous damping resulting from the string motion in a fluid is expressed by a fractional derivative. In this study, the fractional derivative is defined in the Caputo sense because it requires the normal boundary conditions to solve the problem. Using the method of separation of variables, a set of eigenfunctions is identified, and the response of the system is written as a linear combination of these functions. The properties of the eigenfunctions are used to reduce the space-time differential equation of the system into a set of infinite fractional differential equations defined in time domain only. A Laplace transform technique is used to obtain the fractional Green's function and a Duhamel integral type expression for the response of the system. For stochastic analysis, the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic behavior of the system. Several special cases are considered and closed form expressions are found for these cases. The approach is general and it can be applied to all those systems for which the existence of eigenmodes is guaranteed.