Structural reliability theory rationally considers uncertainties that emerge during the analysis and design of ship structures, in contrast to the traditional methods which assume that all parameters affecting the structural strength and load are deterministic values. Determination of the probability of failure is one of the most significant aspects of the reliability theory. Within the introductory part of this work, an overview of the previous scientific research work regarding the considered topic is given, as well as the brief description of different currently utilized reliability analysis methods. Various existing methods are characterized by a different accuracy levels regarding the probability of failure assessment and by various computational timeframes. Within the scope of this work, an efficient reliability analysis method is proposed, which requires significantly lower computational timeframes and which provides sufficiently accurate results with respect to the existing reliability analysis methods. Proposed method is based on determination of the performance function’s probability density function, since the probability of failure can be determined by its integration within the range of minus infinity to zero. Determination of the considered probability density function is performed through two main steps. Within the first step its statistical moments are determined by utilization of the modified (within this work) dimension reduction method. Within the second step an appropriate form of the probability density function is sought, which satisfies statistical moments calculated within the first step. It is assumed thereby that probability density function can be expressed as normalized product of two normal cumulative distribution functions. Additionally, within the scope of this work, analytical expressions for determination of arbitrary statistical moments of the assumed probability density function are derived. Those expressions form the basis of the nonlinear system of equations, whose solution represents four unknown parameters of the assumed probability density function. Furthermore, expressions for determination of the: probability of failure sensitivity, design point and modal correlations (system reliability), are given. Proposed probability analysis method is implemented within the FASTREL computer program and it is verified and validated on a number of examples from the relevant literature. Various examples of application of the proposed method are also given and described.