Machining simulation machine having a display means, for displaying a state of movement of a nozzle with respect to a workpiece to be machined which is instructed by a laser beam machining program on said display means by simulating said laser beam machining program, comprising: a modeling means for producing a solid model of said workpiece to be machined by laser beam machining in a three-dimensional virtual space based upon a workpiece raw material shape instructed by said laser beam machining program, and for producing a solid model of said nozzle in said three-dimensional virtual space by reading a three-dimensional shape of a nozzle to be used at the time of machining on said workpiece out of a machining parameter memory; a chip model producing means for modeling a chip model at an edge of said solid model of said nozzle produced on said three-dimensional virtual space through a predetermined gap between the solid model of the nozzle and the chip model, and for modeling a virtual object for connecting said solid model of said nozzle and said chip model therebetween; a simulation execution means for controlling to move said solid model of said nozzle with respect to said solid model of said workpiece together with said chip model and said virtual object in said three-dimensional virtual space according to an instruction of said laser beam machining program so as to simulate said laser beam machining program; a nozzle/workpiece interference judging means for judging an interference between said solid model of said nozzle and said solid model of said workpiece during simulation of said laser beam machining program through said simulation execution means, and for outputting a signal indicating a program error of said laser beam machining program causing an interference between said nozzle and said workpiece if said interference between said solid model of said nozzle and said solid model of said workpiece is judged; a main control portion for judging as to whether or not a trace machining is instructed in said laser beam machining program during said simulation of said laser beam machining program through said simulation execution means; and a trace machining propriety judging means for judging a state of an interference between said chip model and said solid model of said workpiece if said main control portion judges the instruction of said trace machining in said laser beam machining program, and outputting a predetermined signal indicating a program error of said laser beam machining program causing that said nozzle has lost said workpiece for continuing said trace machining when said state of said interference is judged to be released. a modeling means for producing a solid model of said workpiece to be machined by laser beam machining in a three-dimensional virtual space based upon a workpiece raw material shape instructed by said laser beam machining program, and for producing a solid model of said nozzle in said three-dimensional virtual space by reading a three-dimensional shape of a nozzle to be used at the time of machining on said workpiece out of a machining parameter memory; a chip model producing means for modeling a chip model at an edge of said solid model of said nozzle produced on said three-dimensional virtual space through a predetermined gap between the solid model of the nozzle and the chip model, and for modeling a virtual object for connecting said solid model of said nozzle and said chip model therebetween; a simulation execution means for controlling to move said solid model of said nozzle with respect to said solid model of said workpiece together with said chip model and said virtual object in said three-dimensional virtual space according to an instruction of said laser beam machining program so as to simulate said laser beam machining program; a nozzle/workpiece interference judging means for judging an interference between said solid model of said nozzle and said solid model of said workpiece during simulation of said laser beam machining program through said simulation execution means, and for outputting a signal indicating a program error of said laser beam machining program causing an interference between said nozzle and said workpiece if said interference between said solid model of said nozzle and said solid model of said workpiece is judged; a main control portion for judging as to whether or not a trace machining is instructed in said laser beam machining program during said simulation of said laser beam machining program through said simulation execution means; and a trace machining propriety judging means for judging a state of an interference between said chip model and said solid model of said workpiece if said main control portion judges the instruction of said trace machining in said laser beam machining program, and outputting a predetermined signal indicating a program error of said laser beam machining program causing that said nozzle has lost said workpiece for continuing said trace machining when said state of said interference is judged to be released.