The article contains a survey of methods of the mobile development with the FMX Application platform, which allows to build multi-platform solutions for the efficient Human-Computer Interaction. The test projects illustrate some important conclusions regarding the design and testing of mobile applications for iOS and Android operating systems. They demonstrate navigation controls designed in the skeumorphic and flat manner with some comparisons based on interviews with users in several age ranges. Test apps provide also touch gestures, sensor integration and connections to remote internet data sources. Some additional considerations about the localization and internationalization of the mobile applications built with the FMX platform were also presented. The proposed implementation of the software engineering methods for the mobile application development provides new insights, valuable for software developers dealing with the new FMX platform on iOS and Android.